Question

Which of the following is true for the relation f(x) = x2 + 8? Only the inverse is a function. Both the equation and its inverse are functions. Only the equation is a function. Neither the equation nor its inverse is a function.

Answer 1

ANSWER

Only the equation is a function

EXPLANATION

$f(x)=x^2+8$ is graphed above with its inverse $f^{-1}(x)=\pm \sqrt{x-8}$.

We perform the vertical line test for both the equation and its inverse.

The equation $f(x)=x^2+8$ passed the vertical line hence it is a function.

However, $f^{-1}(x)=\pm \sqrt{x-8}$ failed the vertical line test, hence it is not a function.