College Algebra, 4th Edition

Cumulative Review Exercises Chapters P–7

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

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

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

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

5. Solve the equation $\log { }_5(x-1)+ \log { }_5(x-2)=3 \log { }_5\sqrt[3]{6}.$

6. Express

   $$\log { }_a\sqrt[3]{x\sqrt{yz}}$$

   in terms of logarithms of x, y, and z.

7. Solve the inequality ${\displaystyle \frac{x}{x-2}}\ge 1.$

8. 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.

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

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

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

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

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

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

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

15. Find ...