Finding the inverse of a function

A function is  a special mapping where every element from set A (the domain) is mapped exactly to one element in set B (the range).

Domain refers to the x values that the function occupies, and range referring to the y values. For example: A function of 1/x does not have any values of x=0 or y=0 because these are the asymptotes of the equation.

Therefore... for every value of A to map to set B, the domain and range must specify this i.e:
 Domain:   x ∈ R, x ≠0
 Range:       y ∈ R, y ≠0

 Now every element from set A maps to elements in set B and the equation f(x) = 1/x {x ∈ R, x ≠0} and is now a function.

It is regarded as a one-to-one function because every element of the range comes exactly from one element in the domain.

Finding the inverse of a function:

The example function will be: 2x²-7

1.Set the function equal to y:

y=2x²-7

2.Rearrange to make x the subject:

y=2x²-7

y+7=2x²

0.5(y+7)=x²

x=√(0.5(y+7))

3.Replace (x=) with (f^-1(x)=) and replace (y) with (x)

x=√(0.5(y+7))

f^-1(x)=√(0.5(y+7))

f^-1(x)=√(0.5(x+7))

The inverse of a function graphically, is literally just f(x) reflected in the line y=x.

For example:

"https://en.wikipedia.org/wiki/Inverse_function#/media/File:Inverse_Function_Graph.png"

As shown above, the function just gets reflected in the line y=x to give the inverse function.