Question

The inverse of f(x) is a function. true or false

Answer 1

The statement: The inverse of f(x) is a function is:

True Statement.

Explanation:

The necessary condition that guarantees that a inverse of a function is again a function is:

" The function must be a one-to one function "

Otherwise the inverse may not be a function.

From the given graph of the function we see that the function is a one-to-one function as it passes the horizontal line test i.e. any line passing through the co-domain and parallel to x-axis should intersect the graph atmost once.

Yes, the inverse of the given function F(x) is again a function.

Answer 2

The answer is True.

Explanation:

Since there is only one y for every value of x and only one x for every value of y, both this graph and it's inverse would both be functions.