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An inverse function is the normal function reflected about the line, y = x, such that the points are interchanged. For instance, if we are given a point at (8, 0) and we want to find the inverse, then the inverse points become (0, 8).

So, g⁻¹(7) represents the y-ordinate of g(x) at y = 7.
In short, g⁻¹(7) is -7.

Now, for a function, we first have to interchange the y and x-values and then solve for y.

Let .





So,

Now, if we multiply a function by its inverse, then for when it satisfies the domain, it will be simply whatever number is being referred to.

Example: Find .
The answer will be x, because an inverse function undoes the function in the same way square roots undo square numbers, provided that the value satisfies the inside function.

Thus, satisfies the inverse function, so our answer will simply be -1.