91Ó°ÊÓ

The functions in Exercises \(11-28\) are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\) $$ f(x)=2 x+3 $$

Use the given conditions to write an equation for each line in point slope form and slope-intercept form. Slope \(=-3,\) passing through \((-2,-3)\)

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\) $$ f(x)=x^{2}+2 x \text { from } x_{1}=3 \text { to } x_{2}=5 $$

In Exercises 1–30, find the domain of each function. $$ f(x)=\frac{1}{\frac{4}{x-1}-2} $$

Use the given conditions to write an equation for each line in point slope form and slope-intercept form. Slope \(=-5,\) passing through \((-4,-2)\)

In Exercises 1–30, find the domain of each function. $$ f(x)=\frac{1}{\frac{4}{x-2}-3} $$

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\) $$ f(x)=x^{2}-2 x \text { from } x_{1}=3 \text { to } x_{2}=6 $$

The functions in Exercises \(11-28\) are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\) $$ f(x)=3 x-1 $$

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(2 \sqrt{3}, \sqrt{6}) \text { and }(-\sqrt{3}, 5 \sqrt{6})$$

Determine whether each equation defines y as a function of x. $$ x^{2}+y^{2}=25 $$