Inverse
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:
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:
The logarithm tells us what the exponent is!