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

1 Answer
Sep 14, 2017

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).