Finding the Inverse

2. 1st example, begin with your function

f(x) = 3x – 7 replace f(x) with y

y = 3x - 7

Interchange x and y to find the inverse

x = 3y – 7 now solve for y

x + 7 = 3y

= y

f-1(x) = replace y with f-1(x)

Finding the inverse

3. Because the inverse of a function will return x when you plug in y, the range of the original function will be the domain of its inverse. Although every problem can not be solved using this conversion method, still it will be effective for some time. So we need to interchange the domain and range. In other words, applying $f$ and then $g$ is the same thing as doing nothing. Functions are said to be inverse of each other if f o g = g o f.. Finding Inverse Functions. Find more Mathematics widgets in Wolfram|Alpha. This applet shows the inverse relation of a function. If function f is not a one-to-one then it does not have an inverse. Inverse Functions: The strategy in the process of verifying or checking two inverse functions is based on finding the composite function between both functions. Our goal is to convert an Inverse trigonometric function to another one. Therefore, the domain of the inverse function, , will be [-3, ∞) as well. 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