Inverse Functions

The inverse of (a,b) is (b,a).
Functions are said to be inverse of each other if f _o g = g _o f.

Finding Inverse Functions

ex.

f(x) = 3x - 4
y = 3x - 4 replace f(x) with y
x = 3y - 4 replace x with y and y with x.
3y = x + 4 solve for y

y = (x+4)/3 replace y with f^-1(x)

f^-1(x) = (x+4)/3

The inverse function of 3x - 4 is (x+4)/3.

To test if the example above are inverse of each other, do the inverse function test.

Functions are said to be inverse of each other if f _o g = g _o f.

f(x) = 3x - 4

f _o g = f (g(x))

g(x) = f^-1(x) = (x+4)/3

f(x) = 3x - 4
g _o f = g (f(x))

= g ( 3x - 4 )

They are inverse of each other.

Graph of Inverse Functions:
If the graph of the function f is known then the graph of f^-1 is reflected across the line

y = x. ( or f(x) = x)

ex.