Still Confused?

Try reviewing these fundamentals first.

Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

Function notation (Advanced)- Home
- UK Year 10 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, 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)$f\left( x \right) = \frac{{3x}}{{2 + x}}$

14.

Functions

14.1

Function notation (Advanced)

14.2

Operations with functions

14.3

Adding functions

14.4

Subtracting functions

14.5

Multiplying functions

14.6

Dividing functions

14.7

Composite functions

14.8

Inequalities of combined functions

14.9

Inverse functions

14.10

One to one functions

14.11

Difference quotient: applications of functions

We have over 1410 practice questions in UK Year 10 Maths for you to master.

Get Started Now