Math Lesson 16.6.6 - Other Functions that have an Inverse

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Welcome to our Math lesson on Other Functions that have an Inverse, this is the sixth lesson of our suite of math lessons covering the topic of Inverse Functions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Other Functions that have an Inverse

Other functions that have an inverse include exponential and logarithmic functions, trigonometric functions (we explain these in the later chapters of this Math course), reciprocal functions, etc. For example, an exponential function will have a logarithmic one as an inverse and vice-versa. Let's consider an example to clarify this point.

Example 7

1. Find the inverse of the function f(x) = 3 log x.
2. Plot the graph of f(x) and f - 1(x) in the same figure. Are they symmetrical to each other in respect to y = x?

Solution 7

1. We have
   f(x) = 3 log⁡x
   log⁡x = f(x)/3
   x = 10^f(x)/3
   f^-1 (x) = 10^x/3
2. The domain of f(x) is the positive part of real numbers. Therefore, the range of f - 1(x) will also be the positive part of real numbers. Giving some values in the domain to each function we obtain the following figure that contains the two graphs of f(x) and f - 1(x) and the line y = x.

You have reached the end of Math lesson 16.6.6 Other Functions that have an Inverse. There are 6 lessons in this physics tutorial covering Inverse Functions, you can access all the lessons from this tutorial below.

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