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Algebra

Domain and range of a functionAlgebra

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Function notation (Advanced)- Home
- Sixth Year Maths
- 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, 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.

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

1.

Functions

1.1

Function notation

1.2

Operations with functions

1.3

Adding functions

1.4

Subtracting functions

1.5

Multiplying functions

1.6

Dividing functions

1.7

Composite functions

1.8

Inequalities of combined functions

1.9

Inverse functions

1.10

One to one functions

1.11

Difference quotient: applications of functions

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