Understanding the Domain of Composite Functions

The video tutorial explains how to find the domain of composite functions. It begins with an introduction to composite functions using f(x) and g(x) as examples. The video then discusses the domain restrictions of individual functions and how these affect the domain of the composite function f(g(x)). Through examples involving rational and square root functions, the tutorial demonstrates how to determine the domain of composite functions, emphasizing the importance of considering the domain restrictions of both the inner and outer functions.

What is the domain of the function g(x) = 1/x?

• All negative numbers

• All real numbers

• All real numbers except 0

• All positive numbers

For the function f(x) = 4/(x+2), which value of x is not allowed?

• x = -2

• x = 0

• x = 4

• x = 2

In the composite function f(g(x)), why can't x be zero?

• Because it makes f(x) undefined

• Because it makes g(x) undefined

• Because it makes both f(x) and g(x) undefined

• Because it makes the composite function zero

What happens when you plug x = -1/2 into the composite function f(g(x))?

• It results in a valid output

• It makes g(x) undefined

• It makes f(x) undefined

• It makes the composite function undefined

How do you express the domain of a composite function in interval notation?

• By listing all possible x values

• By using inequalities

• By using union of intervals

• By using set notation

In the example f(x) = 5/(x-3) and g(x) = 2/x, what is the domain of g(x)?

• All real numbers

• All real numbers except 0

• All real numbers except 3

• All real numbers except -3

For the composite function f(g(x)) where f(x) = 5/(x-3), what x value makes the function undefined?

• x = 3

• x = 2/3

• x = -3

• x = 0

In the example with f(x) = x^2 + 3 and g(x) = sqrt(4-x), what is the domain of g(x)?

• x ≤ 4

• x ≥ 4

• x < 0

• x > 0

Why does the composite function f(g(x)) have restrictions even if f(x) is a polynomial?

• Because f(x) has a square root

• Because g(x) is a polynomial

• Because f(x) is undefined for some x

• Because g(x) has a square root

What is the domain of the composite function f(g(x)) in the final example?

• x = 4

• x ≤ 4

• All real numbers

• x ≥ 4