Question
If f(x) satisfies the relation 2f(x) +f(1-x) = x2 for all real x , then f(x) is
The correct answer is: ![fraction numerator 2 x minus 1 plus x squared over denominator 3 end fraction](data:image/png;base64,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)
We have given that
2f(x) +f(1-x) = x2 - - -- - - - - -(i)
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
2f(1-x) + f(x) = (1-x)2
2f(1-x) + f(x) = 1 + x2 – 2x - - - - - -(ii)
Multiplying the equation(i) by 2 we get,
4f(x) + 2f(1-x) = 2x2 - - - - - - (iii)
Subtracting equation (ii) from (iii)
3f(x) = x2 + 2x -1
So,
![f left parenthesis x right parenthesis equals fraction numerator x squared plus 2 x minus 1 over denominator 3 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAAnCAYAAADQBdBUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAxFJREFUeNrtnDFoFEEUhocgIUgQRERERDiCSIoQSCEiEgQRCSkkYBEsJAgiIUg6K7GwCSlCEDsLCwtBJEg4QkCCSAhBEBGxEBsrsbO4QkIIxPe4pyzr7MzsZnZ2du//4Ce53bvlzdu3M++93Tulepd90S5pizSkADDQR5olfYQrgAs7cAGwMU56BzcAEyclR2mVcOyLpFekjuRCn0g3Ixr7WdIDsQtYHNWWYCkDnqWmSYPyeliCcjqS8T8n3ZGkHhhmkjXSkYIVU1HOkD5HWAH2HLdJC5rtj2TfXzhIzlXk2J0D2I1A8QiXuicSr2dITzTOSSuEYy/I8lPUbgSKR66RluT/K6SNSBw7QHovSW4VdiNQNLyRspcz+mMeHGmTjaOk16SrHu32YVfPB8q8lKQjEVyBLQmSoYrtRqBk9C+WSipF8ziWE+anpMMR2B0sUGYzMnMTC/K5UPDVuyonhvsXHzwsPUUdy4npS9KhSOz2Hih9qexbyVS4XfB4W4Gm0uNS9iYdPKm6jaUqHNt2LMFD2e01UDjz/iX6krga+GSPFjRkjLRZ8mD7SSukU5p9L2RcoXFJMqu0u3CLgIPiRyIghuXvqKH2d2VTAgY0gCmJ4jSLpLkDHvtegfwGRMpD0n3N9nXSJc32PG1n7khuwMX1ZyW1ViXLs46spTpc2879cpy8a3ne9joIwFfSac32PUvy69p23oWL6w+XxL8z9u1ZPuvadi4jUPahUvUf50lvM06GaelhXNrOWHoaAuckzwwzRtYdT9e2M5LZhvBYdR+LUznK4zxt5zk5DmhA1TORsU/XcMvbdkbDrSFwy37AsH87kYPkbTuHaOGDAPDs8NPynjrcFIyRyzLzckXJz8p+Iy2rcHeGvbEs/ROX9vpdlb8Nv2jIfXoBriSnUlUjL+XrdRvImAwEhKUDFwAbLZnFAdDC98RmJE+ZgDtAmnSXeR4uASb4KxvXVfe7PeNwB7AxKMECgBX8cA+wMiIJLQD/4N9IuaG6D67zMz/cqf1OugXXgCT8rHFblhoWd2on6zaIP3DqNxUG4zxPAAAA8XRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5mPC9taT48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+MjwvbW4+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjwvbXJvdz48bW4+MzwvbW4+PC9tZnJhYz48L21hdGg+4zczxgAAAABJRU5ErkJggg==)
Therefore option (b) is correct.
We have to find the value of f(x)
By replacing x by (1-x) in equation (i)we get,
Multiplying the equation(i) by 2 we get,
Subtracting equation (ii) from (iii)
So,
Therefore option (b) is correct.
Related Questions to study
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
If f:R->R be a function whose inverse is (𝑥+5)/3 , then what is the value of f(x)
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
Let A= {x, y, z} and B= { p, q, r, s}, What is the number of distinct relations from B to A ?
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f(g)
Name the property of equality the statement illustrates.
If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
Name the property of equality the statement illustrates.
If ∠P ≅ ∠Q, then ∠Q ≅ ∠P.
Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Note: All functions are relations but all relations are not functions.
Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Note: All functions are relations but all relations are not functions.
Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
Rate of Change:___________
Initial Value:______________
Independent Variable:______
Dependent Variable:________
EQ of Line:________________
Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10 packages of buns. Think of the linear function that demonstrates the profit based on the number of hotdogs sold
Rate of Change:___________
Initial Value:______________
Independent Variable:______
Dependent Variable:________
EQ of Line:________________
Sketch a graph modelling a function for the following situation:
A dog is sleeping when he hears the cat “meow” in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn’t find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog’s speed in terms of time.
Sketch a graph modelling a function for the following situation:
A dog is sleeping when he hears the cat “meow” in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn’t find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog’s speed in terms of time.
In the given diagram, m∠1 ≅ m∠3
Prove that ∠POR ≅ ∠QOS.
![](data:image/png;base64,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)
In the given diagram, m∠1 ≅ m∠3
Prove that ∠POR ≅ ∠QOS.
![](data:image/png;base64,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)
When a new laptop became available in a store, the number sold in the first week was high. Sales decreased over the next two weeks and then they remained steady over the next two weeks. The following week, the total number sold by the store increased slightly. Sketch the graph that represents this function over the six weeks.
When a new laptop became available in a store, the number sold in the first week was high. Sales decreased over the next two weeks and then they remained steady over the next two weeks. The following week, the total number sold by the store increased slightly. Sketch the graph that represents this function over the six weeks.
Graph the following functions by filling out the
chart using the inputs ( x values) that you think are appropriate.
Y = 0.25x + 1
X |
|||||
Y |
Graph the following functions by filling out the
chart using the inputs ( x values) that you think are appropriate.
Y = 0.25x + 1
X |
|||||
Y |
Graph the following functions by filling out the x / y chart using the inputs (x values) that you think are appropriate.
Y= x2 + 2
X |
|||||
Y |
Graph the following functions by filling out the x / y chart using the inputs (x values) that you think are appropriate.
Y= x2 + 2
X |
|||||
Y |
Is the relation shown in the table a function ? Explain
![](data:image/png;base64,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)
All functions are relations but all relations are not functions.
Is the relation shown in the table a function ? Explain
![](data:image/png;base64,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)
All functions are relations but all relations are not functions.