Question

Which of the following is true for the relation f(x)=x^2+8

Answer 1

Answer: Both the equation and its inverse are functions.

Explanation

Given the equation:

$f\mleft(x\mright)=x^2+8$

we can use the vertical line test to determine if it is a function:

As no vertical line touches the graph, then it is a function. Additionally, the inverse function can be calculating by interchanging the x and y variables in the original function:

$x=y^2+8$$x-8=y^2$$y=\sqrt{x-8}$

If we do the same vertical test for the inverse function we will see that both are function.