### Home > APCALC > Chapter 6 > Lesson 6.1.1 > Problem6-9

6-9.

Write the equation of the inverse, $f ^{–1}(x)$, for each of the following functions. Homework Help ✎

1. $f ( x ) = 2 ^ { x }$

Solve for x: log2y = x
Then 'switch' the input and the output.

f −1(x) = log2x

1. $f ( x ) = \operatorname { log } _ { 3 } x$

This is the reverse of part (a).

1. $f ( x ) = \operatorname { log } _ { e } x$

Recall that e is a constant. (It's value is between 2 and 3)

f −1(x) = ex

1. $f ( x ) = 5 \cdot 9 ^ { x }$

Be sure to divide both sides by 5 before you solve for x .