Inverse means the opposite in effect. The reverse of.

It is a general idea in mathematics and has many meanings. Here are a few.

The Inverse of Adding is Subtracting

Adding moves us one way, subtracting moves us the opposite way.

Example: 20 + 9 = 29 can be reversed by 29 − 9 = 20 (back to where we started)

And the other way around:

Example: 15 − 3 = 12 can be reversed by 12 + 3 = 15 (back to where we started)

Additive Inverse

The additive inverse is what we add to a number to get zero.

Example: The additive inverse of −5 is +5, because −5 + 5 = 0.

Another example: the additive inverse of +7 is −7.

The Inverse of Multiplying is Dividing

Multiplying can be "undone" by dividing.

Example: 5 × 9 = 45 can be reversed by 45 / 9 = 5

It works the other way around too, dividing can be undone by multiplying.

Example: 10 / 2 = 5 can be reversed by 5 × 2 = 10

Multiplicative Inverse

The multiplicative inverse is what we multiply a number by to get 1.

It is the reciprocal of a number.

Example: The multiplicative inverse of 5 is 15, because 5 × 15 = 1

But Not With 0

We can't divide by 0, so don't try!

Example: 5 × 0 = 0 cannot be reversed by 0/0 = ???

Inverse of a Function

Doing a function and then its inverse will give us back the original value:

banana f() to apple f()-inverse back to banana
When the function f turns the apple into a banana,
Then the inverse function f-1 turns the banana back to the apple


Here we have the function f(x) = 2x+3, written as a flow diagram:


The Inverse Function goes the other way:


So the inverse of:   2x+3   is:   (y−3)/2

Read Inverse of a Function to find out more.

Inverse Sine, Cosine and Tangent

Example: the sine function


The sine function sin takes angle θ and gives the ratio opposite hypotenuse

The inverse sine function sin-1 takes the ratio oppositehypotenuse and gives angle θ

Read Inverse Sine, Cosine, Tangent to find out more.

The Inverse of an Exponent is a Logarithm

Read logarithmsto find out more, but basically:

2^3=8 becomes log_2(8)=3

The logarithm tells us what the exponent is!