Function Composition and Simplification

The video tutorial explains how to determine the composition of two functions, f(x) = 2x - 1 and g(x) = x^2 - 4. It covers the process of calculating f(g(x)) and g(f(x)) by substituting one function into the other and simplifying the result. The tutorial provides a detailed, step-by-step approach to solving these compositions, including distributing terms and combining like terms. The video concludes with a summary of the results for both compositions.

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

• f(x) = 2x + 1, g(x) = x^2 + 4

• f(x) = x^2 - 4, g(x) = 2x - 1

• f(x) = 2x - 1, g(x) = x^2 - 4

• f(x) = x^2 + 1, g(x) = x - 4

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

• Substitute g(x) into f(x)

• Find the derivative of g(x)

• Find the inverse of f(x)

• Substitute f(x) into g(x)

What expression do we get after substituting g(x) into f(x)?

• x^2 + 4

• 2x - 1

• x^2 - 4

• 2(x^2 - 4) - 1

What is the simplified form of f(g(x))?

• 2x^2 - 9

• x^2 - 9

• 2x^2 - 8

• x^2 - 8

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

• Find the derivative of f(x)

• Find the inverse of g(x)

• Substitute f(x) into g(x)

• Substitute g(x) into f(x)

What expression do we get after substituting f(x) into g(x)?

• 2x - 1

• (2x - 1)^2 - 4

• x^2 - 4

• (x^2 - 4)^2

What is the result of expanding (2x - 1)^2?

• 4x^2 - 1

• 4x^2 + 4x + 1

• 4x^2 + 1

• 4x^2 - 4x + 1

What is the simplified form of g(f(x))?

• 4x^2 + 4x - 3

• 4x^2 - 3

• 4x^2 - 4x - 3

• 4x^2 + 3

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

• 2x^2 - 9

• 4x^2 - 4x - 3

• x^2 - 9

• 2x^2 - 8

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

• 4x^2 - 4x - 3

• x^2 - 4

• 4x^2 - 3

• 2x^2 - 9