Understanding Function Composition and Inverses

The video tutorial explores the functions f(x) = 2x - 3 and g(x) = 1/2x + 3. It evaluates the compositions f(g(x)) and g(f(x)), demonstrating the step-by-step substitution and simplification process. The results show that f(g(x)) = x + 3 and g(f(x)) = x + 3/2, indicating that f(x) and g(x) are not inverses of each other, as neither composition returns the original input x.

What are the given functions f(x) and g(x) in the video?

• f(x) = 2x - 3, g(x) = 1/2x + 3

• f(x) = 2x + 3, g(x) = 1/2x - 3

• f(x) = x/2 + 3, g(x) = 2x - 3

• f(x) = 3x - 2, g(x) = 2x + 1/2

What is the result of evaluating f(g(x))?

• 2x - 3

• 2x + 3

• x + 3

• x - 3

What is the first step in evaluating f(g(x))?

• Substitute f(x) into g(x)

• Substitute g(x) into f(x)

• Add f(x) and g(x)

• Multiply f(x) and g(x)

What is the result of evaluating g(f(x))?

• 2x + 3

• x - 3/2

• x + 3/2

• 2x - 3

What is the first step in evaluating g(f(x))?

• Substitute f(x) into g(x)

• Add f(x) and g(x)

• Multiply f(x) and g(x)

• Substitute g(x) into f(x)

What conclusion can be drawn from the results of f(g(x)) and g(f(x))?

• They are both zero

• They are not inverses of each other

• They are equal

• They are inverses of each other

What is a key characteristic of inverse functions?

• They are always equal

• They have the same slope

• They return to the original input

• They always add up to zero

Why are f(x) and g(x) not inverses of each other?

• They have the same slope

• They are equal

• They do not return to the original input

• They are both linear

What happens when you apply g to an x value and then f?

• You get 2x

• You get x - 3

• You get x + 3

• You return to the original x

What happens when you apply f to an x value and then g?

• You return to the original x

• You get x + 3/2

• You get x - 3/2

• You get 2x