Learn How to Find the Inverse of a Function: Step-by-Step Guide with Example

Which equation is the inverse ofy = x^2 + 16

C.

To find the inverse of a function, we need to switch the variables x and y and then solve for y. So let’s start by switching x and y in the equation y = x^2 + 16:

x = y^2 + 16

Now we need to solve for y. To do this, we’ll use inverse operations to isolate y on one side of the equation.

x – 16 = y^2 (Subtract 16 from both sides)
±√(x – 16) = y (Take the square root of both sides)

Note that we must include both the positive and negative square roots since a quadratic function does not have an inverse that is also a function. Therefore, the inverse of y = x^2 + 16 is:

y = ±√(x – 16)

More Answers: