Finding the Inverse of a Function

Definition: The process of finding the function that maps the range back the domain of the original function.

Example: Find the inverse of y = (x² +3)/16.


Step 1: Interchange the variables.

x = (y²+3)/16

Step 2: Make y the subject of the equation.

Multiply both sides by 16:
16x = (y²+3)

Subtract 3 from both sides:
16x – 3 = y²

Find the square root of both sides:
y = √(16x-3)

y^-1 = √(16x-3)
where the domain consists of all x ≥ 3/16 (note this was the range of the original function, that is, y ≥ 3/16).

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