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Question

Let f colon R rightwards arrow R be given by f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis to the power of 2 end exponent minus 1 comma x greater or equal than negative 1. Then the set of values of x for which f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis is given by

  1. {0}    
  2. {-1,0}    
  3. left curly bracket negative 1 right curly bracket       {0}    
  4. {0,1}    

Hint:

f colon R rightwards arrow R indicates a function “f”, Having domain ”R” and co-domain “R” (Range). That means in simple we can imagine that “The set of all possible input values for x is the domain of the function. The set of all output values of y is the range of the function.”

The correct answer is: {-1,0}


    The given function f colon R rightwards arrow R be given by f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis to the power of 2 end exponent minus 1 comma x greater or equal than negative 1
    Indicates f(x) will satisfy all values for x greater or equal than space minus 1
    w e space h a v e space t o space p r o v e space space f left parenthesis x right parenthesis space equals space f to the power of negative 1 end exponent left parenthesis x right parenthesis space
f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction space equals space fraction numerator 1 over denominator left parenthesis x space plus space 1 right parenthesis squared minus 1 end fraction
f o r space space f left parenthesis x right parenthesis space equals space f to the power of negative 1 end exponent left parenthesis x right parenthesis space comma space t h e space r e v e r s e space f u n c t i o n space s h o u l d space a l s o space h o l d space t h e space s a m e space v a l u e s space i. e space x space greater or equal than space minus 1
s u b s t i t u t i n g space left parenthesis 0 comma negative 1 right parenthesis space i n space f to the power of negative 1 end exponent left parenthesis x right parenthesis space comma space w e space g e t space
f to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space minus 1 space equals space f left parenthesis x right parenthesis
space
    Thus, the set of values of x for which f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis is given by (0, -1) for x greater or equal than -1 .

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