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Question

If f left parenthesis x right parenthesis equals open parentheses 10 minus x to the power of 7 end exponent close parentheses to the power of 1 divided by 7 end exponent, then f o f left parenthesis x right parenthesis equals

  1. 10    
  2. x    
  3. x to the power of 7 end exponent    
  4. 10 to the power of 7 end exponent    

Hint:

The composition of functions f(x) and g(x) where g(x) is acting first is represented by f(g(x)) or (f ∘ g)(x). It combines two or more functions to result in another function. In the composition of functions, the output of one function that is inside the parenthesis becomes the input of the outside function. i.e.,

  • In f(g(x)), g(x) is the input of f(x).
  • In g(f(x)), f(x) is the input of g(x).

The correct answer is: x


     Givenf left parenthesis x right parenthesis equals open parentheses 10 minus x to the power of 7 end exponent close parentheses to the power of 1 divided by 7 end exponent
    To findf o f left parenthesis x right parenthesis
    rightwards double arrow f o f left parenthesis x right parenthesis space equals space f left parenthesis f left parenthesis x right parenthesis right parenthesis
rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis space equals space left parenthesis 10 space minus space left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of 7 right parenthesis to the power of 1 over 7 end exponent rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis space equals space left parenthesis space 10 space minus space open square brackets left parenthesis 10 space minus space x to the power of 7 right parenthesis to the power of 1 over 7 end exponent close square brackets to the power of 7 right parenthesis to the power of 1 over 7 end exponent
rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis space equals space left parenthesis 10 space minus space 10 space plus space x to the power of 7 right parenthesis to the power of 1 over 7 end exponent
rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis space equals space left parenthesis x to the power of 7 right parenthesis to the power of 1 over 7 end exponent
rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis space space equals space x
     Thus, f o f left parenthesis x right parenthesis equals x 

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