Question
The range of the function ![f left parenthesis x right parenthesis equals square root of left parenthesis x minus 1 right parenthesis left parenthesis 3 minus x right parenthesis end root text is end text](data:image/png;base64,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)
Hint:
Here we have to find the range of f(x)=
. Just solve the function and find the solution then find the range for the function.
The correct answer is: ![left square bracket 0 comma 1 right square bracket](data:image/png;base64,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)
Here we have to find that the range of ![square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAATCAYAAABIgIm/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAApVJREFUeNrtmT9IHEEUxocgRxALxQSLWIiIWIRDUEGJIoKFiIWIgaQKEhEJIpYWBgIWkRQaiJ2CRSA2/gERFSRIOMKhiKaUWFhapAikMIeoyTfwhGVuZ/aN3Lhzx33ww3Pn3P3mzeybeaMQfJWBf0W8g60XYE8UlbfaBsOatjdgxmPvM+RRFKj/SD0Cv+mnqiRI58EE/E5eC80/S6Ng3XDjRg86WA/egh+a9iaQYvjvAlvgAmTAT/ARVMbcP51/luTaNxhyvZEC4IM+g5GIhT1FgTD5l30dAAnlezse9FH1z1IN+AUehrR9AGOepRrTAI4ra52N/z8e9G38Lmv1JFjQtMlZ2RFy/bXmQdPUFtcAtoGvDP+qasGJI782sVL9s3QMegyzMqFpOwJVgd+HwHzMb2BCeZNM/gX5H6J1sNehZ26sEqZMUBZy7Sk4ByWav7kymJKDPkufu+8ycxwMoNQlw79aLE849mwTq0v1Qh1YIqPtStt7MGe42VWEsV3QSTvDSkbgc3HqkIsBvFUF6Af71A+X3rmxyhrAKRpAWecdKG1noDliYTeloAl6YFLcn3KZQoPZad+xb06sjClUVvo3gVzcCk4N6fN21jzTtMnrK5QaXnoygOomwORfVcahZ26sIjcxsnj9Qp8/gXcRD9Ztw+WubQOU0uw9vMdC2DSAY+TZtoxI0kbGhWxipfrP0iL4S2+drP0aIh4eVgg/ppOMoIk+KrTjHkBOIf8NPKcYPKCTGbmUvHLg1TZWkYV8ObgGq4J/PpgO5G2Zo9fAk5DvLRvKkVwNnGnjoDuKSivrjqwLNyllZuhkps+BX9tYsY/SUpZb5+Jhdrz+s9RCA1htcfNR4fe/Y+S6MVLA/rM0KIrKC/0HCXEd6Lk+nVQAAADKdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zcXJ0PjxtZmVuY2VkPjxtcm93PjxtaT54PC9taT48bW8+LTwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mZW5jZWQ+PG1mZW5jZWQ+PG1yb3c+PG1uPjM8L21uPjxtbz4tPC9tbz48bWk+eDwvbWk+PC9tcm93PjwvbWZlbmNlZD48L21zcXJ0PjwvbWF0aD4pklFLAAAAAElFTkSuQmCC)
f (x) = ![square root of open parentheses x minus 1 close parentheses open parentheses 3 minus x close parentheses end root](data:image/png;base64,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)
= ![square root of negative x 2 plus 4 x minus 3 end root](data:image/png;base64,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)
=![square root of negative x 2 plus 4 x minus 4 plus 1 end root](data:image/png;base64,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)
= ![square root of 1 minus open parentheses x minus 2 close parentheses 2 end root](data:image/png;base64,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)
The maximum value of f (x) is 1,
when (x – 2) = 0.
So, we can write Fmax= 1
Now,
It is minimum when,
(x – 2)2 = 1
(x – 2) = ± 1 [ since, x = √a2, then x = ± a]
At, positive, x -2 = 1 => x = 3
And at negative, x -2 = -1 => x = 1,
Therefore, x = 3, x = 1
So, Minimum =
– 1 = 0
Therefore, the Range = [0, 1].
In this question, we have to find the range of f(x)=. Here solve the function and find when function is at maximum and minimum.
Related Questions to study
The range of the function ![sin invisible function application open parentheses sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x close parentheses comma vertical line x vertical line less or equal than 1 text is end text](data:image/png;base64,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)
The range of the function ![sin invisible function application open parentheses sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x close parentheses comma vertical line x vertical line less or equal than 1 text is end text](data:image/png;base64,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)
The domain of the function ![f left parenthesis x right parenthesis equals log subscript e invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis text is end text](data:image/png;base64,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)
The domain of the function ![f left parenthesis x right parenthesis equals log subscript e invisible function application left parenthesis x minus left square bracket x right square bracket right parenthesis text is end text](data:image/png;base64,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)
If
, and the period of
is
, then n is equal to
If
, and the period of
is
, then n is equal to
Domain of definition of the function ![f left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x squared end fraction plus log subscript 10 invisible function application open parentheses x cubed minus x close parentheses comma text is end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPEAAAAmCAYAAAAV8H2eAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABRJJREFUeNrtnEFIFUEYxwcJiQhBJEQkBBGREBEiREQkiAgREaGDhwgRIkTEW3SIDhGIB5HoEh06SHgJEZEQQkJERJCIEJEgooN0CDp4EBHhNR/ve7Rv3dmdeTu7O6v/H3zo7nu7+97M/5uZb+abJwQI4ra0j9KOpB1L+y5tTlodigaAfPBZ2rC0as+5TmmrKBoA8s0higCA/NIsbR/FAED+qJc2ynFxP4oDgPxQ8NkUigSAfFIrbUjatrQ+FAcA+eUqOzJwb7R0Iu2rtLsoEhDFMYrAWdqk/UIxRDMubdrwmmm+Lu90iOLkFnBDV36qpP3N8Ds4p3MqkPoAEW9VeL9Nvj4vrEu7L+0SlwVlcP2U9hD+lkjjuBXzHpRJ91oUVxGyxBmd3+MWjWyXhVz6gJ0V3vOmtI0cCatX2goPn8kog2sgpzGj68TRlTcufuDAd4mjc2t1RQ574CnUG/y3kws7Dhv8JQGcWFjUFVEj7aW0Rw58p0p1bq2uKF94IeD8jLSJmPeetBD3ALPKdt2JbejKiwsTj5nr/Lm0JwHnV3mI6WdM8YFf8GteuqWtwQczd2IKC/ZEcVmG/g4qrqX62mHH+MHxpu1GwYauvCHQTkJlnobO/WXbzGHckSdkiGRRlGcojXheo8T/asV1X0T5JNgoTzL4qRbqDQQFDQPxnbiLHbKdj9v5uNv3vjY+3+sR1PsE6iGurkraOOYGoSnBcrehc5O62glpYEOhBP/rAedPQ66hibBZ/v9ORCt0Ah/M1Ik/iLMTdHS85Dv3ThFf2nZiW7pKg6R17i9b6oFrTW9SxReaFjbxSRRTEilrpi5lJy6cE4vz/XSFEdTzBfUcfxQCStOJTXRlSyciQ537n0+pvpu+EXEkXTwGNx32EFP8wcPWyDCczr4nLmiKrmDh2XGH07q6SpO4OjetV0r1fctzF606NxnhYZSqBepRvNbDw7TZiFYDE1vZO7FuT3zEIzOdZ5O4nnHvFMQAh2n7AUN5G7pKi6R1HlavTzkmj+SVUK+zqZYCaMJjWdoVbjV2QoYZE3wfkG1MPBgwbFv0nVsNmOyqVTx7nnVTUAh6nTVRxyO9bsu6SoM0dF6ICHW1huhUkapN70GL8tdE8cfk6nyt7rziHkj2yN6Jb4nirHMpiaeDj/29YT/XVz0LiCZ1aAfXseHnWhLl2zd72Rls6ipp4up8gctmKEa9joWEumVQmuXlkNe3PLFANTt9Y8D7FrjSveQt7TIJxyttmSPRtmTo8KXhLX2W3RBxkXAO+H3b3AAcGj7r0Dcsrwq4RxxdJY0NnVfqxCXNnHIj0qDT2vyOeM9F2gCRFCTicd34xjHqI2K9gua5E4u6cg2VzhdEwj/tNMcts06q2GNhnlI2I9zIaXWJPOxLXubeV3AvQMejMXviS4revBJduYZK552ifCNRItAQYBh+lRp9PNnjOrQV85v4n3YZ9RtjOjEx/b9yweq7UZzd1gsMGBBurTE38JCr+ZzG/X5oJpomZGo5ZFsX+MVQYAAtBew55MSt3As1nEPnDUvMoYaUfhGFJk4nIUtgwhtRnGF1wYnJcWmGsQbVAoAetO65FjLMs4XuFjVy4DZUCwB60NoeTcg0peDEhMmWOeSCA6AB9YwTPgdKEte2zAGQa2ihfTOgFwwjzS1qAIAIKD2wxdCJbeDaljkAcksWe5Jd2zIHwLl07KRwbcscAHBiA1zbMgcAnNgA17bMgQvMP2KrzlIDUTtVAAABpHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtbj4zPC9tbj48bXJvdz48bW4+NDwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZnJhYz48bW8+KzwvbW8+PG1zdWI+PG1pPmxvZzwvbWk+PG1uPjEwPC9tbj48L21zdWI+PG1vPiYjeDIwNjE7PC9tbz48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bXN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZmVuY2VkPjxtbz4sPC9tbz48bXRleHQ+JiN4QTA7aXMmI3hBMDs8L210ZXh0PjwvbWF0aD7TRtZQAAAAAElFTkSuQmCC)
Domain of definition of the function ![f left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x squared end fraction plus log subscript 10 invisible function application open parentheses x cubed minus x close parentheses comma text is end text](data:image/png;base64,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)
Range of the function ![f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text](data:image/png;base64,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)
Range of the function ![f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAAqCAYAAADlA1TjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABFJJREFUeNrtnE9kHGEUwD8rIiJKVEVVhKiqPdTSQ0VFL1UVVRGqVk8VKiKqh1I9VFWVyKGieuuhKipURVVEqaiKiBIVVRW9V2895FARYfueeaOT2W9mvj+zk51978eT7OzOfN/uvvfN+7efUnxpkOyBrIOcVILAkArINMhX+SgEzuzKRyBw5QLIZ/kYBI4cpxhguAPey3mQtyA7FNtsgdyQr1hI4hTIMhlBJ4B3sTpIHz2uknHX5asWdCv/CsgRh3MbBc/VZ7whkG/ydfNhEmRWc/wxPReCyn+6AIU0nU8rDU4CfGZgSnMg8vgmyHONUsWlVSuyyXxaZQAj5AYJjLgM8pT+vwiyesguie98XA2gB+QLBccCMz6qIL2JmZCjOSh8luQ5nzzG6wd5B3JJVIEnd1SQCjzTJkGpz3xsxxsm5Zf2DqaE+XB0O+ptYAC+87EZDwP7FyC9ogb5M52Q0Uhjls4rClz93pMCYD58MwcXyEch85iP6XgYaL8B6RJV9aMSy1oounVvOF5vvUWuSJxjKkhvRhXsCsjCIRlAXvMxHW9Zuad2hUjG4g/J98hqgkpcc7zmWZC1Fs+7G2QJ5ITmuUV6X0VyGPPxCZrbhV2a7y8VZLBWaCHJOybT0kUDh4pepb815Z9LXiNDEHiAd6J5FdRA/lICIEtRMWjfih17AjJXlAFM0OoUBycw43nt2w7xg1BOJsh7mKJFr9vwvHGQ17Fj10FeFjXxhyD3NMc/gIxqjtuU+bEiuSq6USpc2jgGadXvddS/u7Fjj1SQQra5A2Di4RPdeYxdwKWYzxhN1+2kWLFpmb+brmPru5bNhy0ji/QZj3t8vyHPEq5jAmawrkYeY6PitiYhk2UAm7HrGLNNFhxnPyNoNi3z74mulc4AbNs4MIasOM7jpwq6dLtoXDS+a4bBfxRc+fttB6/QicrSABDTMn8rDKAh4iQ22LRx7DmOWyE9i7521EIH4rGE9e8gzpHfpGMnI5AxKfOLC1RebNo4XO8Acf0bMcj+pGWBsOiIFfEfKvjhUyb1lGgbV4CkjkLTMr8EweXEto1j3jEG0Okf6t2QowGE3FeGO35g8HIr4bmkNKhNmX/GwqKF9sCljWOQXtdnOZZO/3DRfOVpABVT1xuzQGMJz+kKYbZlfimElSsI9mnjwNx9WAeoKbPepCT9Q6+h6mEAkymu/QGw9aEn5fmNiA9oW+YvohXCNXiWneGaDSCPNo54JXg/Q1GT9G+EDNHGAMLvdp/Ozdz0AK39d8ZrytAM54LsDPdfscc4vnG0Usz/m7QpTCn7doa5lNiineD8w/GaOtj4yAp0TyaYr37cd4ZDV2dACSzppJ3hQjDv/UA1d1YKQpOidNLOcCEL5HZKAVFIXfk7fWc4MQCGyM5wYgDskZ3hxABYIzvDiQGwh/vOcGIAzOG8M5wYAHM47wwnBsAczjvDiQEwh/vOcGIAjJGd4dKDaEHDP/gg2OhsbVlPAAABeHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4yPC9tbj48L21yb3c+PG1yb3c+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21mcmFjPjxtbz47PC9tbz48bWk+eDwvbWk+PG1vPiYjeDIyMDg7PC9tbz48bWk+UjwvbWk+PG10ZXh0PiYjeEEwO2lzJiN4QTA7PC9tdGV4dD48L21hdGg+bZDdIAAAAABJRU5ErkJggg==)
Range of the function ![f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text](data:image/png;base64,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)
Range of the function ![f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text is end text](data:image/png;base64,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)
The domain of ![sin to the power of negative 1 end exponent invisible function application open parentheses log subscript 3 invisible function application x close parentheses text is end text](data:image/png;base64,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)
The domain of ![sin to the power of negative 1 end exponent invisible function application open parentheses log subscript 3 invisible function application x close parentheses text is end text](data:image/png;base64,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)
The domain of the function ![f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript invisible function application open parentheses x squared minus 1 close parentheses text is end text](data:image/png;base64,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)
The domain of the function ![f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript invisible function application open parentheses x squared minus 1 close parentheses text is end text](data:image/png;base64,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)
If
, then
is
Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.
If
, then
is
Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.