When given f(x)=3x+12, find f(f^-1(x))

Question

asked Oct 12, 2020 205k views

1 Answer

Alisia · Answer 1 · 2020-10-17T16:16:17+0000

Answer:

$\large\boxed{f\bigg(f^(-1)(x)\bigg)=x}$

Explanation:

$\text{Find}\ f^(-1)(x)$

$f(x)=3x+12\to y=3x+12$

exchange x to y and vice versa:

x=3y+12

solve for y:

3y+12=x subtract 12 from both sides

3y=x-12 divide both sides by 3

$y=(x-12)/(3)\to f^(-1)(x)=(x-12)/(3)$

$f\bigg(f^(-1)(x)\bigg)\to$ replace x in f(x) with the expression
(x-12)/(3)

$f\bigg(f^(-1)(x)\bigg)=3\cdot(x-12)/(3)+12=x-12+12=x$