Inverse Functions (Learn Algebra 2)

Master inverse functions in this comprehensive math tutorial! Mario's Math Tutoring explains what inverse functions are, how to find them, and how to verify they are inverses of one another using function composition (f(g(x)) = x and g(f(x)) = x). Learn about the graphical relationship between a function and its inverse (reflection over y=x) and how to use the Horizontal Line Test to determine if an inverse is also a function. We'll work through multiple examples, including those with domain restrictions, perfect for algebra 2, pre-calculus, or college algebra students!

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Timestamps:
00:00 What is the inverse of a function?
0:47 How to prove that the functions are inverses of each other.
1:17 Introductory example for finding the inverse of f(x)=2x-1
2:00 What does the inverse graph of a function look like?
4:32 What is the vertical line test and what does it test for?
5:13 What is the Horizontal line test and what does it test for?
6:42 Example 1 find the inverse of f(x)=3x^5
7:24 Example 2 Find the inverse of y=3x+6
7:53 Example 3 Find the inverse of y=4/5 x +10
8:37 Example 4 Show the functions are inverses a(x)=6x+5, b(x)=(x-5)/6
9:58 Example 5 Show c(x)=2x^2 -1, d(x)=sq.rt.((x+1)/2)
11:18 Example 6 Is the Inverse of f(x)=3x^3 -2 a function?
12:32 Example 7 Is the Inverse of g(x)=-2x^2 + 4 a function?
13:02 Example 8 Find the inverse and state domain f(x)=3x^2 -5, x greater than or equal to 0.

Related YouTube Videos to Help You:

Inverse Functions Complete Guide
   • Inverse Functions (Complete Guide)  

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