Finding the Composition of Two Functions with Rational Exponents

The video tutorial explains the concept of function composition, demonstrating how to calculate F(G(x)) and G(F(x)). It shows that both compositions result in X to the 4th power. The tutorial also discusses the domain of these functions, noting that there are no restrictions such as division by zero or roots, making the domain all real numbers.

What is the result of composing F of G when F(x) = x^(2/3) and G(x) = x^6?

• x^4

• x^3

• x^6

• x^5

In the composition G of F, what is the expression for G(x) if F(x) = x^(2/3)?

• x^(2/3)

• x^(1/3)

• x^4

• x^6

What is the result of the composition G of F when F(x) = x^(2/3) and G(x) = x^6?

• x^6

• x^3

• x^4

• x^5

What is the significance of the order in which functions are composed in this example?

• The order changes the result

• The order affects the domain

• The order does not affect the result

• The order makes the function undefined

Why is the domain of the composed functions all real numbers?

• Because there are no restrictions like division by zero or roots

• Because there is division by zero

• Because there are no roots involved

• Because the functions are undefined