91Ó°ÊÓ

In Exercises \(1-18\), find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$\left(-\frac{1}{4},-\frac{1}{7}\right) \text { and }\left(\frac{3}{4}, \frac{6}{7}\right)$$

A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is bent into a square. Express the sum of the areas of these squares, \(A\), as a function of the length of the cut, \(x\).

Find the domain of each function. $$f(x)=\sqrt{x+2}$$

Graph each equation . Let \(x=-3,-2,-1,0\) \(1,2,\) and 3. $$y=2 x-4$$

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 $$ f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x $$. $$f(x)=x^{3}-1$$

use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(=-2,\) passing through \((0,-3)\)

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=\sqrt{x} \text { from } x_{1}=9 \text { to } x_{2}=16$$

Determine whether the graph of each equation is symmetric with respect to the \(y\) -axis, the \(x\) -axis, the origin, more than one of these, or none of these. $$y=x^{2}-2$$

Determine whether the graph of each equation is symmetric with respect to the \(y\) -axis, the \(x\) -axis, the origin, more than one of these, or none of these. $$x=y^{2}+6$$

Find the domain of each function. $$g(x)=\frac{1}{\sqrt{x-3}}$$