3.7 Inverse functions  (Page 8/9)

$f(x)=-3x+5$

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

$f(x)=\left|x+1\right|$

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

$f(2)$

$f(\mathrm{-2})$

If $f(x)=\mathrm{-2},$ then solve for $x.$

If $f(x)=1,$ then solve for $x.$

$\frac{h(2)-h(1)}{2-1}$

$\frac{h(a)-h(1)}{a-1}$

$f(x)=\frac{2}{3x+2}$

$f(x)=\frac{x-3}{x^2-4x-12}$

$f(x)=\frac{\sqrt{x-6}}{\sqrt{x-4}}$

Graph this piecewise function: $f(x)=\{\begin{array}{l}x+1x<-2\\ -2x-3x\ge -2\end{array}$

$f(x)=4x-3$

$f(x)=10x^2+x$

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

Find the local minimum of the function graphed in [link] .

Find the local extrema for the function graphed in [link] .

For the graph in [link] , the domain of the function is $\left[-3,3\right].$ The range is $\left[-10,10\right].$ Find the absolute minimum of the function on this interval.

Find the absolute maximum of the function graphed in [link] .

$f(x)=4-x,g(x)=-4x$

$f(x)=3x+2,g(x)=5-6x$

$f(x)=x^2+2x,g(x)=5x+1$

$f(x)=\sqrt{x+2},g(x)=\frac{1}{x}$

$f(x)=\frac{x+3}{2},g(x)=\sqrt{1-x}$

$f(x)=\frac{x+1}{x+4},g(x)=\frac{1}{x}$

$f(x)=\frac{1}{x+3},g(x)=\frac{1}{x-9}$

$f(x)=\frac{1}{x},g(x)=\sqrt{x}$

$f(x)=\frac{1}{x^2-1},g(x)=\sqrt{x+1}$

$H(x)=\sqrt{\frac{2x-1}{3x+4}}$

$H(x)=\frac{1}{{(3x^2-4)}^{-3}}$

$f(x)={(x-3)}^2$

$f(x)={(x+4)}^3$

$f(x)=\sqrt{x}+5$

$f(x)=-x^3$

$f(x)=\sqrt[3]{-x}$

$f(x)=5\sqrt{-x}-4$

$f(x)=4\left[\left|x-2\right|-6\right]$

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

$g(x)=f(x-1)$

$g(x)=3f(x)$

$f(x)=3x^4$

$g(x)=\sqrt{x}$

$h(x)=\frac{1}{x}+3x$

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

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

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

$f(x)=9+10x$

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

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

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 $f(a+1)-f(1)$ in simplest form.

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 $\frac{f(b)-f(a)}{b-a}$ in simplest form.

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

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

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 $f(x)=-2\left|x-1\right|+3.$

$f(x)=3x-5$

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

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 $f^{-1}(x).$