Question

hello I need help with this questiongiven f(x)=3x+2 and the inverse F-1 (x)= 1/3 (x-2) determine f(f(x)).

Answer 1

Given f(x) = 3x + 2, to find f(f(x)) we need to substitute x = f(x) into f(x) as follows:

$\begin{gathered} f\mleft(x\mright)=3x+2 \\ f(f(x))=3f(x)+2 \\ f(f(x))=3(3x+2)+2 \\ f(f(x))=3\cdot3x+3\cdot2+2 \\ f(f(x))=9x+6+2 \\ f(f(x))=9x+8 \end{gathered}$