91Ó°ÊÓ

Verify that the functions $f\left(x\right)=3-2x$and $g\left(x\right)=-\frac{1}{2}\left(x-3\right)$are inverses of each other by showing that $f\left(g\left(x\right)\right)=x$and $g\left(f\left(x\right)\right)=x$. Give any values of x that need to be excluded from the domain of f and the domain ofg.

Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.

$\ln 27$

For the given functions f and g, find:

$a)f∘gb)g∘fc)f∘fd)g∘g$

State the domain of each composite function.

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

What rate of interest compounded annually is required to triple an investment in 10 years?

The graph of an exponential function is given. Match each graph to one of the following functions.

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.

$5^{-x}=25$

Use the given function $f\left(x\right)=\frac{1}{2}\ln (x+3)$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 $f^{-1}$.

For the given functions f and g, find:

$a)f∘gb)g∘fc)f∘fd)g∘g$

State the domain of each composite function.

$f\left(x\right)=\frac{3}{x-1}, g\left(x\right)=\frac{2}{x}$

Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.

$\ln \sqrt[5]{6}$

Find the exact value of the logarithm without using a calculator.

$\ln \left(\sqrt{e}\right)$