Inverses
Finding the Inverse
To find an inverse symbolically:
1. Substitute y for f(x).
2. Interchange the x and y variables - this is the foundation behind inverses.
3. Solve the new equation for y.
4. Substitute f-1(x) for y.
Example 1 Find the inverse of the function f(x) = 5x -2.
Step 1. Write the original function using y notation.
y = 5x -2
Step 2. Interchange x and y.
x = 5y - 2
Step 3. Solve the new equation for y.
Step 4. Simplify if possible and change to inverse function notation.
