Question

What is the inverse of f(x) = x2 + 5 and is it a function?

Answer 1

Answer:

Step-by-step explanation:

The inverse of an equation is only a function if the original function is one-to-one.  Meaning it passes the horizontal line test.  Our equation is a parabola.  While this original is in fact a function, it is not one-to-one.  So that means that the inverse will not be a function.  Let's find the inverse first, then we will verify its non-function status.

To find the inverse, switch the x and the y and solve for the new y:

$x=y^2+5$ and

$x-5=y^2$ which means that

$y=+/-\sqrt{x-5}$

Because you are taking the square root of y, you need to allow for both the positive and the negative of the square root of x - 5.  Graph these 2 equations in your calculator and you will see that if we do not first restrict the domain of the original equation, our inverse will not be a function.