Function Composition and Inverses

This video tutorial explains how to verify if two functions are inverses of each other. It involves checking that f(g(x)) = x and g(f(x)) = x. The video provides three examples: linear functions, fifth root functions, and cube root functions, demonstrating the process of substitution and simplification to confirm the inverse relationship. The tutorial concludes with encouragement to continue practicing math skills.

What is the first step in verifying that two functions are inverses of each other?

• Calculate F(G(x)) and simplify to see if it equals x

• Check if F(x) equals G(x)

• Ensure both functions are linear

• Calculate G(F(x)) and simplify to see if it equals x

What is the first step in verifying that two functions are inverses of each other?

• Ensure both functions are linear

• Check if F(x) equals G(x)

• Calculate F(G(x)) and simplify to see if it equals x

• Calculate G(F(x)) and simplify to see if it equals x

In the first example, what is the expression for F(G(x)) before simplification?

• x - 3 over 6

• x plus 3

• 6x + 3

• 6 times (x - 3) over 6 plus 3

What is the result of simplifying F(G(x)) in the first example?

• x - 3

• x + 3

• x

• 6x

What is the result of simplifying F(G(x)) in the first example?

• x - 3

• 6x

• x + 3

• x

In the first example, what is the expression for F(G(x)) before simplification?

• x plus 3

• 6 times (x - 3) over 6 plus 3

• x - 3 over 6

• 6x + 3

In the first example, what is the expression for G(F(x)) before simplification?

• x - 3

• 6x + 3 over 6

• x plus 3

• 6 times x

What is the result of simplifying G(F(x)) in the first example?

• x - 3

• 6x

• x + 3

• x

What is the result of simplifying G(F(x)) in the first example?

• x

• x + 3

• x - 3

• 6x

In the first example, what is the expression for G(F(x)) before simplification?

• 6x + 3 over 6

• x - 3

• x plus 3

• 6 times x