Hi San,

If you think of a function as a process where you give the function some input and it yields a result then the inverse of this function answers the question "Here is the result, what was the input?" For example if the function is f(x) = x² then an inverse is g(x) = √x. If you give x = 5 to the function f it yields
f(5) = 5² = 25 and if you give x = 25 to the function g it yields g(25) = √25 = 5. (You may wonder why I didn't say ±5 but the symbol √ designates the positive square root.)

If you have studied logarithms then another example you have seen is f(x) = 10^x and g(x) = log₁₀(x).

In trigonometry an example is f(x) = tan(x) and g(x) = tan^-1(x). If you have a right triangle and x is the measure of one of the other two angles then tan(x) is the ratio of the opposite side over the adjacent side. For the inverse function, if you have a right triangle and A is one of the vertices where the angle is not a right angle, let x be the ratio of the opposite side over the adjacent side. The measure of the angle at A is g(x) = tan^-1(x).

One last example is the game show Jeopardy. In this game the contestants must perform an inverse operation. The host tells them an answer and they must give the question.

Penny