91Ó°ÊÓ

Find the inverse of the function$$\begin{gathered} f\left(x\right)=\sqrt{r^2-x^2} \\ 0≤x≤r \end{gathered}$$

In Problems 71– 86, use the given functionf to:

(a) Find the domain of f.

(b) Graph f.

(c) From the graph, determine the range and any asymptotes of f.

(d) Find $f^{-1}$, the inverse of f.

(e) Find the domain and the range of$f^{-1}$.

(f) Graph $f^{-1}$.

$f\left(x\right)=2^{\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+4$

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:

${\log }_5\left(x\right)+{\log }_3\left(x\right)=1$

A function $f$has an inverse function. If the graph of $f$ lies in quadrant I in which quadrant does the graph of $f^{-1}$ lie?

Determine the exponential function whose graph is given.

If $f\left(x\right)=\ln x,g\left(x\right)=e^x$, and $h\left(x\right)=x^2$, find:

(a)role="math" localid="1647337775231" $\left(f∘g\right)\left(x\right)$. What is the domain of $f∘g$?

(b) $\left(g∘f\right)\left(x\right)$. What is the domain of $g∘f$ ?

(c) $(f∘g)\left(5\right)$

(d)$(f∘h)\left(x\right)$. What is the domain of $f∘h$?

(e) $\left(f∘h\right)\left(e\right)$

In Problems 71– 86, use the given functionf to:

(a) Find the domain off.

(b) Graphf.

(c) From the graph, determine the range and any asymptotes off.

(d) Find $f^{-1}$, the inverse off.

(e) Find the domain and the range of$f^{-1}$.

(f) Graph $f^{-1}$.

$f\left(x\right)=-3^{x+1}$

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:

${\log }_2\left(x\right)+{\log }_6\left(x\right)=3$

If $f\left(x\right)={\log }_{2}x,g\left(x\right)=2^x$, and $h\left(x\right)=4x$, find:

(a) role="math" localid="1647339659415" $\left(f∘g\right)\left(x\right)$. What is the domain of $f∘g$?

(b) $\left(g∘f\right)\left(x\right)$. What is the domain of $g∘f$?

(c) $\left(f∘g\right)\left(3\right)$

(d) $\left(f∘h\right)\left(x\right)$. What is the domain of $f∘h$?

(e) $\left(f∘h\right)\left(8\right)$

In Problems $85-88$, determine the exponential function whose graph is given.