91Ó°ÊÓ

Verify that the functions $f\left(x\right)=4x-8$and $g\left(x\right)=\frac{x}{4}+2$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 that need to be excluded from the domain of f and the domain ofg.

(a) How long does it take for an investment to double in value if it is invested at 8% compounded monthly?

(b) How long does it take if the interest is compounded continuously?

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.

$2^x=10$

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:$8^{6+3x}=4$

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

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

$\ln \left(e^3\right)$

Verify that the functions $f\left(x\right)=2x+6$and $g\left(x\right)=\frac{1}{2}x-3$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 ofx that need to be excluded from the domain of f and the domain of g.

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

$\ln \sqrt[4]{\frac{2}{3}}$

(a) How long does it take for an investment to triple in value if it is invested at 6% compounded monthly?

(b) How long does it take if the interest is compounded continuously?

In Problems 29 – 44, for the given functions f and g, find:

(a)$f∘g$

(b)$g∘f$

(c)$f∘f$

(d) $g∘g$

State the domain of each composite function.

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