# Cumulative Review Exercises Chapters P–7

Let $f\text{}(x)={x}^{2}{-}^{}3x+2.$ Find $\frac{f\text{}(x+h)-f\text{}(x)}{h}}.$

Sketch the graph of $f\text{}(x)=\sqrt{x+1}-2.$

Let $f\text{}(x)=2x-3.$ Find the inverse function ${f}^{-1}$. Verify that $f\text{}({\text{}f}^{-1}(x))=x.$

Sketch the graph of $f\text{}(x)={\left({\displaystyle \frac{1}{2}}\right)}^{x+2}.$

Solve the equation $\mathrm{log}{}_{5}(x-1)+\mathrm{log}{}_{5}(x-2)=3\mathrm{log}{}_{5}\sqrt[3]{6}.$

Express

$$\mathrm{log}{}_{a}\sqrt[3]{x\sqrt{yz}}$$in terms of logarithms of

`x`,`y`, and`z`.Solve the inequality $\frac{x}{x-2}}\ge 1.$

The current

`I`in an electric circuit is given by$$I={\displaystyle \frac{V}{R}}(1-{e}^{-0.3t}).$$Use natural logarithms to solve for

`t`.

In Problems 9–12, solve each system of equations.

$\{\begin{array}{lllll}1.4x& -& 0.5y& =& 1.3\\ 0.4x& +& 1.1y& =& 4.1\end{array}$

$\{\begin{array}{rrrrrrl}2x& +& y& -& 4z& =& 3\\ x& -& 2y& +& 3z& =& 4\\ -3x& +& 4y& -& z& =& -2\end{array}$

$\{\begin{array}{rcl}y& =& 2-\mathrm{log}\text{}x\\ y-\mathrm{log}(x+3)& =& 1\end{array}$

$\{\begin{array}{rcl}y& =& {x}^{2}-1\\ 3{x}^{2}+8{y}^{2}& =& 8\end{array}$

Find the determinant of the matrix $\left[\begin{array}{rrr}1& 4& 7\\ 2& 5& 8\\ 3& 6& 9\end{array}\right]$.

Use Cramer’s Rule to solve the system of equations.

$$\{\begin{array}{rrr}2x-3y& =& -4\\ 5x+7y& =& 1\end{array}$$Find ...

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