In this lesson, we learn how to prove that two functions are inverses of each other. The key is to use composition - plug one function into the other and evaluate. If the result is x both ways, then the functions are inverses. The transcript shows an example of proving the inverse functions f(x) and g(x), with step-by-step explanation and cancellation of terms. By understanding this process, we can confidently prove the inverse of any pair of functions.
Proving two functions are inverses of each other
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Questions answered by this video:
How do I show that two functions are inverses of each other?
How do you find the composition of two functions?
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This video shows how to prove that two functions are inverses of each other by showing that f(g(x))=x and g(f(x))=x.