3.7 Inverse functions  (Page 7/9)

$f(x)=\sqrt[3]{x-1}$ and $g(x)=x^3+1$

$f(x)=-3x+5$ and $g(x)=\frac{x-5}{-3}$

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

$f(x)=\sqrt[3]{3x+1}$

$f(x)=\mathrm{-5}x+1$

$f(x)=x^3-27$

Find $f\left(0\right).$

Solve $f(x)=0.$

Find $f^{-1}\left(0\right).$

Solve $f^{-1}\left(x\right)=0.$

Sketch the graph of $f^{-1}.$

Find $f(6)\text{ and }{f}^{-1}(2).$

If the complete graph of $f$ is shown, find the domain of $f.$

If the complete graph of $f$ is shown, find the range of $f.$

If $f(6)=7,$ find $f^{-1}(7).$

If $f(3)=2,$ find $f^{-1}(2).$

If $f^{-1}\left(-4\right)=-8,$ find $f(-8).$

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

Find $f\left(1\right).$

Solve $f(x)=3.$

Find $f^{-1}\left(0\right).$

Solve $f^{-1}\left(x\right)=7.$

Use the tabular representation of $f$ in [link] to create a table for $f^{-1}\left(x\right).$

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

$f(x)=x^3-1$

Find the inverse function of $f(x)=\frac{1}{x-1}.$ Use a graphing utility to find its domain and range. Write the domain and range in interval notation.

To convert from $x$ degrees Celsius to $y$ degrees Fahrenheit, we use the formula $f(x)=\frac{9}{5}x+32.$ Find the inverse function, if it exists, and explain its meaning.

The circumference $C$ of a circle is a function of its radius given by $C(r)=2\pi r.$ Express the radius of a circle as a function of its circumference. Call this function $r(C).$ Find $r(36\pi )$ and interpret its meaning.

A car travels at a constant speed of 50 miles per hour. The distance the car travels in miles is a function of time, $t,$ in hours given by $d(t)=50t.$ Find the inverse function by expressing the time of travel in terms of the distance traveled. Call this function $t(d).$ Find $t(180)$ and interpret its meaning.

$\left\{(a,b),(c,d),(e,d)\right\}$

$\left\{(5,2),(6,1),(6,2),(4,8)\right\}$

$y^2+4=x,$ for $x$ the independent variable and $y$ the dependent variable

Is the graph in [link] a function?

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

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