### 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.

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

Solve for $x$: $\log_2y=x$
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 $3$)

$f^{ −1}\left(x\right) = e^{x}$

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

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