Question

Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? The function f has an inverse f –1 that is even. The function f has an inverse f –1 that is odd. The function f has an inverse f –1, but we can't tell whether it's even or odd. f –1 is not a function. We can't tell whether or not f has an inverse.

Answer 1

`f^(-1)` is not a function.

Explanation:

Consider the provided information.

If a function is Even function that means the graph of the function is symmetric with respect to the y-axis.

So, if (x,y) is on the graph, then (-x, y) is also on the graph.

The graph of even function is not one to one as it not satisfy the horizontal line test.

Even functions are not one-to -one, and therefore do not have inverses.

Or we can say that
`f^(-1)` is not a function.