Exploring Inverse Functions: Part 2

This video tutorial covers inverse functions, focusing on two methods to determine if functions are inverses: using composition and finding the inverse directly. It includes examples to illustrate these methods, such as proving inverses through composition and identifying non-inverse functions. A bonus question is also discussed, verifying a student's claim about inverse functions.

In example seven, what is the composition of f(g(x))?

• x

• x + 1

• 2x

• x - 1

What is the result of composing a function and its inverse?

• Undefined

• x

• 0

• 1

What is the first step in proving two functions are inverses using composition?

• Find the derivative

• Solve for y

• Rewrite the function

• Substitute one function into the other

What is an alternative method to prove two functions are inverses?

• Graphing both functions

• Finding the inverse of one function

• Using derivatives

• Multiplying both functions

How do you start finding the inverse of a function?

• Interchange x and y

• Integrate the function

• Solve for x

• Differentiate the function

In example eight, what is the simplified form of f(g(x))?

• x + 1

• x

• 3x

• x/3

What indicates that two functions are not inverses?

• f(g(x)) = x

• g(f(x)) = x

• f(x) = g(x)

• f(g(x)) ≠ x

In example nine, if f(g(x)) does not equal x, what can be concluded?

• Functions are linear

• Functions are identical

• Functions are not inverses

• Functions are inverses

What is the result of g(f(x)) in example eight?

• 3x

• x/3

• x + 1

• x

What is the correct inverse of g(x) = 4/(x - 2) + 1?

• x/(4 - 2) + 1

• 4/(x - 1) + 2

• 4/(x + 2) - 1

• 4/(x - 2) + 1