Why does the function $f(x) = x^2 + 5$ not have an inverse over the set of all real numbers?

The function's graph does not have a y-intercept.

There are at least two different inputs that produce the same output.

The function is not defined for all possible input values.

The output of the function is always positive.

Which statement best explains why the function $g(x) = \cos(x)$ does not have an inverse over its entire domain?

$g(x)$ is always between -1 and 1.

The function is continuous everywhere.

The function is not one-to-one.

The function is not continuous.

The function does not pass the vertical line test.

The domain of the function is restricted.