1.6 Inverse functions  (Page 9/10)

$f(x)=\left|x-5\right|$

$f(x)=-\left|x-3\right|$

$f(x)=\left|2x-4\right|$

$\left|x+4\right|=18$

$\left|\frac{1}{3}x+5\right|=\left|\frac{3}{4}x-2\right|$

$\left|3x-2\right|<7$

$\left|\frac{1}{3}x-2\right|\le 7$

$f(x)=9+10x$

$f(x)=\frac{x}{x+2}$

$f(x)=x^2+1$

Given $f\left(x\right)=x^3-5$ and $g(x)=\sqrt[3]{x+5}:$

1. Find $f(g(x))$ and $g(f(x)).$
2. What does the answer tell us about the relationship between $f(x)$ and $g(x)?$

$f(x)=\frac{1}{x}$

$f(x)=-3x^2+x$

If $f\left(5\right)=2,$ find $f^{-1}(2).$

If $f\left(1\right)=4,$ find $f^{-1}(4).$

$y=2x+8$

$\left\{(2,1),(3,2),(-1,1),(0,-2)\right\}$

$f(\mathrm{-2})$

$f(a)$

Show that the function $f(x)=-2{(x-1)}^2+3$ is not one-to-one.

Write the domain of the function $f(x)=\sqrt{3-x}$ in interval notation.

Given $f(x)=2x^2-5x,$ find $f(a+1)-f(1).$

Graph the function $f(x)=\{\begin{array}{cc}x+1\text{ if}& -2<x<3\\ -x\text{ if }& x\ge 3\end{array}$

Find the average rate of change of the function $f(x)=3-2x^2+x$ by finding $\frac{f(b)-f(a)}{b-a}.$

$\left(g\circ f\right)(x)$

$\left(g\circ f\right)(1)$

Express $H(x)=\sqrt[3]{5x^2-3x}$ as a composition of two functions, $f$ and $g,$ where $\left(f\circ g\right)(x)=H(x).$

$f(x)=\sqrt{x+6}-1$

$f(x)=\frac{1}{x+2}-1$

$f(x)=-\frac{5}{x^2}+9x^6$

$f(x)=-\frac{5}{x^3}+9x^5$

$f(x)=\frac{1}{x}$

Graph the absolute value function $f(x)=-2\left|x-1\right|+3.$

Solve $\left|2x-3\right|=17.$

Solve $-\left|\frac{1}{3}x-3\right|\ge 17.$ Express the solution in interval notation.

$f(x)=3x-5$

$f(x)=\frac{4}{x+7}$

On what intervals is the function increasing?

On what intervals is the function decreasing?

Approximate the local minimum of the function. Express the answer as an ordered pair.

Approximate the local maximum of the function. Express the answer as an ordered pair.

Find $f(2).$

Find $f(\mathrm{-2}).$

Write an equation for the piecewise function.

Find $F(6).$

Solve the equation $F(x)=5.$

Is the graph increasing or decreasing on its domain?

Is the function represented by the graph one-to-one?

Find $F^{-1}(15).$

Given $f(x)=-2x+11,$ find $f^{-1}(x).$