91Ó°ÊÓ

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

Find the domain of each function. $$ g(x)-\frac{1}{\sqrt{x+2}} $$

Determine whether each function is even, odd, or neither. $$g(x)=x^{2}-x$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--1,\) passing through \((-4,-1)\)

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(-\frac{1}{2},\) passing through the origin

Find the midpoint of each line segment with the given endpoints. $$(-2,-8)\( and \)(-6,-2)$$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) passes through \((-6,4)\) and is perpendicular to the line that has an \(x\) -intercept of 2 and a \(y\) -intercept of \(-4\)

Find the domain of each function. $$ g(x)-\sqrt{5 x+35} $$

Determine whether each function is even, odd, or neither. $$h(x)=x^{2}-x^{4}$$

The functions 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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{1}{x} $$