91Ó°ÊÓ

The graph of a one-to-one function f is given. Draw the graph of the inverse function $f^{-1}$. For convenience (and as a hint), the graph of $y=x$is also given.

Find the domain of the function.

$g\left(x\right)=\ln \left(\frac{1}{x-5}\right)$

Write each expression as a sum and/or difference of logarithms. Express powers as factors.

$\ln \left(x{e}^x\right)$

Credit Card Interest

A department store charges 1.25% per month on the unpaid balance for customers with charge accounts (interest is compounded monthly). A customer charges $200 and does not pay her bill for 6 months. What is the bill at that time?

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

${\left(\frac{4}{3}\right)}^{1-x}=5^x$

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:$e^{1-x}=5$

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

$f\left(x\right)=2^{x+2}$

In Problems 29 – 44, for the given functions fand g, find: $\left(a\right)f∘g\left(b\right)g∘f\left(c\right)f∘f\left(d\right)g∘g$

localid="1647279857360" $f\left(x\right)=\frac{2x-1}{x-2},g\left(x\right)=\frac{x+4}{2x-5}$

In Problem, the graph of a one-to-one function $f$is given. Draw the graph of the inverse function $f^{-1}$. For convenience (and as a hint), the graph of $y=x$is also given.

In Problems 45–52, show that $(f∘g)\left(x\right)=(g∘f)\left(x\right)=x$

$f\left(x\right)=2x;g\left(x\right)=\frac{1}{2}x$