Question

Good morning! Can someone help me real quick please?

For the function `f(x) = x^2 ­ -12`, find `(f @ f^(­-1))(4)`

A. 10
B. 6
C. 0
D. 4

Answer 1

Answer is (D).

Explanation:

As `f(x)=x^2-12`,

`x^2=f(x)+12` and `x=sqrt(f(x)+12)`

hence `f^(-1)=sqrt(x+12)`

and as `(f@g)(x)=f(g(x))`

`(f@f^(-1))(x)=f(f^(-1)(x))=f(sqrt(x+12))`

and `(f@f^(-1))(4)=f(f^(-1)(4))`

= `f(sqrt(4+12)))`

= `f(4)`

= `4^2-12=16-12=4`

Hence, answer is (D).