CPM Homework Help : PC Problem 3-89

Let $f(x)=3^x$ . Evaluate each of the following, or state “impossible” and explain why. It may be helpful to first replace $f$ and $f^{−1}$ with their definitions.

Examples: $f\left(3\right) = 3^{x} = 27$ $f^{−1}\left(9\right)=\log_39=2$

$f(4)$
Step (a):
$f(4) = 3^4$

$f^{-1}(81)$
Step (b):
This means you need to solve $3^x=81$ .

$f(-2)$
Step (c):
$f(-2)=3^{-2}$

$f^{-1}\left(\frac{1}{9}\right)$
Step (d):
$f(?)=\frac{1}{9}$

$f\left(\frac{1}{2}\right)$
Step (e):
$f\left(\frac{1}{2}\right)=3^{1/2}$

$f^{-1}\left(\sqrt{3}\right)$
Step (f):
$f(?)=\sqrt{3}$