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Algebra

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Function notation (Advanced)- Home
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- Functions

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.

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

38.

Functions

38.1

Function notation

38.2

Operations with functions

38.3

Adding functions

38.4

Subtracting functions

38.5

Multiplying functions

38.6

Dividing functions

38.7

Composite functions

38.8

Inequalities of combined functions

38.9

Inverse functions

38.10

One to one functions

38.11

Difference quotient: applications of functions

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