Question

asked Feb 12, 2020 203k views

1 Answer

Bananafish · Answer 1 · 2020-02-19T11:09:28+0000

Answer:

0

Explanation:

METHOD 1.

We know:

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

Therefore

$f\bigg(f^(-1)(0)\bigg)=0$

METHOD 2.

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

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

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)

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

$f\bigg(f^(-1)(0)\bigg)\to$ put x = 0 to
$f\bigg(f^(-1)(x)\bigg)=x$

$f\bigg(f^(-1)(0)\bigg)=0$

METHOD 3.

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

f^(-1)(x)=(x-12)/(3)

Calculate the value of f ⁻¹(x) for x = 0:

f^(-1)(0)=(0-12)/(3)=(-12)/(3)=-4

Calculate the value of f(x) for x = -4:

f(4)=3(-4)+12=-12+12=0