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)
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