Function Composition and Expressions

The video tutorial explains how to find and simplify composite functions f(g(x)) and g(f(x)) using given function rules. It starts with defining the functions f(x) = x - 5 and g(x) = 3x^2 - 4x. The tutorial then demonstrates the process of substituting and simplifying these functions to find the composite functions. The video provides step-by-step instructions for both f(g(x)) and g(f(x)), highlighting the importance of substitution and simplification in solving composite functions.

What is the expression for f(x) given in the video?

• x + 5

• 2x - 5

• 3x^2 - 4x

• x - 5

What is the expression for g(x) as introduced in the video?

• 3x^2 - 4x

• x + 5

• x - 5

• 2x - 5

How do you express f(g(x)) using the given functions?

• g(x - 5)

• f(3x^2 - 4x)

• f(x + 5)

• g(2x - 5)

What is the result of distributing and simplifying f(g(x))?

• 6x^2 - 8x - 5

• 12x^2 - 68x + 95

• 3x^2 - 4x

• 2x - 5

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

• Subtract f(x) from g(x)

• Substitute f(x) into g(x)

• Multiply g(x) by f(x)

• Add f(x) to g(x)

What expression do you substitute into g(x) to find g(f(x))?

• x - 5

• 2x - 5

• x + 5

• 3x^2 - 4x

What is the result of expanding and simplifying g(f(x))?

• 6x^2 - 8x - 5

• 12x^2 - 68x + 95

• 2x - 5

• 3x^2 - 4x

What operation is performed after substituting 2x - 5 into g(x)?

• Division

• Multiplication

• Subtraction

• Addition

What is the coefficient of x^2 in the expression for g(f(x))?

• 2

• 6

• 3

• 12

What is the constant term in the final expression for g(f(x))?

• 20

• -5

• 95

• 75