Find the inverse of f(x) = 6x.
The inverse is
g(x) =
Graph the function and its inverse

Given:

The function is:

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

Step 1: Substitute .

Step 2: Interchange x and y.

Step 3: Isolate variable y.

Step 4: Substitute .

Therefore, the inverse of the given function is and the graphs of these functions are shown below.

Note: The inverse function is .

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.