91Ó°ÊÓ

Solve. If \(f(x)=3 x-10,\) show that \(f^{-1}(x)=\frac{x+10}{3}\)

Solve. If \(f(x)=x^{3}+6,\) show that \(f^{-1}(x)=\sqrt[3]{x-6}\)

Write each expression as a sum or difference of logarithms. Assume that variables represent positive numbers. See Example 5. $$ \log _{5} x^{3}(x+1) $$

Find the total amount Janina has in a college savings account if \(\$ 2000\) was invested and earned \(6 \%\) compounded semiannually for 12 yearsFind the total amount Janina has in a college savings account if \(\$ 2000\) was invested and earned \(6 \%\) compounded semiannually for 12 years.

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to solve these compound interest problems. Find how long it takes a \(\$ 1200\) investment to earn \(\$ 200\) interest if it is invested at \(9 \%\) interest compounded quarterly.

$$ \begin{array}{rl} {\text { Given that } f(-1)=4} & {g(-1)=-4} \\ {f(0)=5} & {g(0)=-3} \\ {f(2)=7} & {g(2)=-1} \\ {f(7)=1} & {g(7)=4} \end{array} $$ Find each function value. $$ \left(\frac{f}{g}\right)(-1) $$

Solve. If \(f(x)=x^{3}-5,\) show that \(f^{-1}(x)=\sqrt[3]{x+5}\).

$$ \begin{array}{rl} {\text { Given that } f(-1)=4} & {g(-1)=-4} \\ {f(0)=5} & {g(0)=-3} \\ {f(2)=7} & {g(2)=-1} \\ {f(7)=1} & {g(7)=4} \end{array} $$ Find each function value. $$ \left(\frac{g}{f}\right)(-1) $$

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to solve these compound interest problems. Find how long it takes a \(\$ 1500\) investment to earn \(\$ 200\) interest if it is invested at \(10 \%\) compounded semiannually.

Write each expression as a sum or difference of logarithms. Assume that variables represent positive numbers. See Example 5. $$ \log _{6} \frac{x^{2}}{x+3} $$