Inverse functions

How to find the inverse of a function:
Switch x and y, and then solve for y
Ex.
f(x) = 5x
x = 5y
y = x/5

An Inverse is just a reflection of a function
The two functions will be symmetric over the line y = x

To determine if the inverse of a function is a function, graph the function, and apply the horizontal line test.
If any horizontal line intersects the function more than once the inverse is not a function

Two functions f and g are inverses of each other if: f(g(x)) = x and g(f(x)) = x

The Domain of a normal function is the range of its inverse, and the Range of a normal function is the domain of its inverse

How to find the inverse of a relation:
Just swap the x and y coordinates around
Ex.
{(-8, 5), (4, -2), (-7, 1)}
Inverse: {(5, -8), (-2, 4), (1, -7)}

Examples of inverses:

ex og ln(x) 
1 og log(x) 
x 
2x og 
2 
x +8 og x —8