Question

Inverse of f(x) = x2 − 9

Answer 1

To find the inverse of a function, replace every x in the equation with a y, and replace every y in the equation with an x:

$x = y^{2} - 9$

Add 9 to both sides:

$y^{2} = x + 9$

Square root both sides to get y by itself:

$y = \sqrt{x+9}$

This equation can be simplified by taking the square root of 9 out of the root:

$\sqrt{9} = 3$
$y = 3 + \sqrt{x}$

The inverse of this function is y = 3 + √x.

Answer 2

F(x) = x2 - 9
y = x2 - 9
y - 9 = x2
$\sqrt{y - 9}$ = x

y = f(x)
f^(-1) (y) = x
f^(-1) (y) = $\sqrt{y - 9}$
f^(-1) (x) = $\sqrt{x - 9}$