Question

Given f(x)=3x+12, what is f(f^-1(3))

Answer 1

Answer:

3

Step-by-step explanation:

We know:

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

Therefore

$f\bigg(f^{-1}(3)\bigg)=3$

Other method.

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

$y=\dfrac{x-12}{3}\to f^{-1}(x)=\dfrac{x-12}{3}$

$f\bigg(f^{-1}(x)\bigg)$ replace x in f(x) with the expression $\dfrac{x-12}{3}$

$f\bigg(f^{-1}(x)\bigg)=3\cdot\dfrac{x-12}{3}+12=x-12+12=x$

$f\bigg(f^{-1}(3)\bigg)$ - put x = 3 to $f\bigg(f^{-1}(x)\bigg)$

$f\bigg(f^{-1}(3)\bigg)=3$