Proving Two Functions are Inverses - Concept

Concept Concept (1)

The definition of a function can be extended to define the definition of an inverse, or an invertible function. It's important to understand proving inverse functions, and the method of proving inverse functions helps students to better understand how to find inverse functions. Students should review how to find an inverse algebraically and the basics of proofs.

Sample Sample Problems (4)

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Proving Two Functions are Inverses - Problem 1

Prove f(x) = 6x − 3 and g(x) = ⅙(x + 3) are inverses.

Problem 1
How to use composition of functions to show two functions are inverses.
Proving Two Functions are Inverses - Problem 2

Prove f(x) = 2(x + 3) and f⁻¹(x) = ½x + 3 are inverses.

Problem 2
How to use composition of functions to show two functions are not inverses.
Proving Two Functions are Inverses - Problem 3
Problem 3
How to use composition of functions to prove that two functions are inverses, including those with domain restrictions.
Proving Two Functions are Inverses - Problem 4
Problem 4
How to use composition of functions to verify that pairs of exponential and logarithmic functions are inverses.