91Ó°ÊÓ

Use the Inverse Function Property to show that f and g are inverses of each other. $$f(x)=\frac{1}{x}, \quad g(x)=\frac{1}{x}$$

Use the function to evaluate the indicated expressions and simplify. $$f(x)=x^{2}+1 ; \quad f(x+2), f(x)+f(2)$$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$g(x)=2 x^{2}+8 x+11$$

Use the Inverse Function Property to show that f and g are inverses of each other. $$f(x)=x^{5}, \quad g(x)=\sqrt[5]{x}$$

Explain how the graph of \(g\) is obtained from the graph off. (a) \(f(x)=|x|, \quad g(x)=3|x|+1\) (b) \(f(x)=|x|, \quad g(x)=-|x+1|\)

Use the function to evaluate the indicated expressions and simplify. $$f(x)=3 x-1 ; \quad f(2 x), 2 f(x)$$

A function is given. Determine the average rate of change of the function between the given values of the variable. $$g(x)=\frac{2}{x+1} ; \quad x=0, x=h$$

Use the function to evaluate the indicated expressions and simplify. $$f(x)=x+4 ; \quad f\left(x^{2}\right),(f(x))^{2}$$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Sketch its graph. (c) Find its maximum or minimum value. $$h(x)=1-x-x^{2}$$

Use the Inverse Function Property to show that f and g are inverses of each other. $$\begin{aligned}&f(x)=x^{2}-4, \quad x \geq 0\\\&g(x)=\sqrt{x+4}, \quad x \geq-4\end{aligned}$$