Question

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

Answer 1

Their point of intersection will always be on the line y = x.

Explanation:

We have a function f(x) and its inverse is the function f⁻¹(x).

The domain and range of a function replaces each other for the inverse of that function.

So if f(x) and f⁻¹(x) are inverse of each other

and f(a) = b

then a = f⁻¹(b)

Another example to make it clear is that

f(5) = 25

f⁻¹(25) = 5

The function and its inverse will intersect each other at the point where f(x) = f⁻¹(x) which is only possible when a = b.

Hence, a function and its inverse will always intersect at a point on the line x=y.