Still Confused?

Try reviewing these fundamentals first.

Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

Function notation (Advanced)Still Confused?

Try reviewing these fundamentals first.

Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

Function notation (Advanced)Still Confused?

Try reviewing these fundamentals first.

Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

Function notation (Advanced)Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Intro Lesson12:05
- Lesson: 111:06
- Lesson: 2a5:00
- Lesson: 2b8:02
- Lesson: 2c15:06
- Lesson: 3a5:12
- Lesson: 3b4:39
- Lesson: 3c4:30

An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.

Basic concepts: Domain and range of a function, Identifying functions, Function notation (Advanced),

Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

- Introduction

• What is “inverse”, and what does “inverse” do to a function?

• Inverse: switch “x” and “y”

• Inverse: reflect the original function in the line “y = x” - 1.
**Graph an inverse**

Given the graph of $y = f\left( x \right)$ as shown,

a)Sketch the graph of the inverse $y = {f^{ - 1}}\left( x \right)$ in 2 ways:

i) by reflecting $f\left( x \right)$ in the line $y = x$

ii) by switching the x and y coordinates for each point on $f\left( x \right)$b)Is $f\left( x \right)$ a function?

Is ${f^{ - 1}}\left( x \right)$ a function? - 2.
**Inverse of a Quadratic Function**

Consider the quadratic function: $f(x) = (x+4)^2 + 2$a)Graph the function $f\left( x \right)$ and state the domain and range.b)Graph the inverse ${f^{ - 1}}\left( x \right)$ and state the domain and range.c)Is ${f^{ - 1}}\left( x \right)$ a function?

If not, describe how to restrict the domain of $f\left( x \right)$ so that the inverse of $f\left( x \right)$ can be a function. - 3.
**Determine the equation of the inverse.**

Algebraically determine the equation of the inverse ${f^{ - 1}}\left( x \right)$, given:a)$f\left( x \right) = - 5x + 4$b)$f\left( x \right) = {\left( {7x - 8} \right)^3} - 1$c)$f\left( x \right) = \frac{{3x}}{{2 + x}}$

We have over 1100 practice questions in Algebra 2 for you to master.

Get Started Now