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 = √(x+9)`

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


`√(9) = 3`

`y = 3 + √(x)`

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

Answer 2

f(x) = x2 - 9
y = x2 - 9
y - 9 = x2

`√(y - 9)` = x

y = f(x)
f^(-1) (y) = x
f^(-1) (y) =
`√(y - 9)`
f^(-1) (x) =
`√(x - 9)`