Function Composition and Simplification

The video tutorial explains how to compose functions with themselves using given functions f(x) = 2x - 1 and g(x) = x^2 - 4. It demonstrates the process of finding f(f(x)) and g(g(x)) by substituting the function rules into themselves and simplifying the expressions. The tutorial provides a step-by-step approach to distribute, combine like terms, and arrive at the final simplified forms of the compositions.

What is the initial step in composing a function with itself?

• Multiply the function by a constant

• Substitute a numerical value into the function

• Write the composition using an alternate form

• Directly simplify the function

When composing f with itself, what is the expression for f(f(x)) before simplification?

• 2x - 1

• x^2 - 4

• 4x - 3

• 2(2x - 1) - 1

What is the result of simplifying f(f(x))?

• x^4 - 8x^2 + 12

• x^2 - 4

• 2x - 1

• 4x - 3

What is the first step in composing g with itself?

• Multiply the function by a constant

• Substitute x^2 - 4 for x

• Directly simplify the function

• Write the composition using an alternate form

What expression do we get for g(g(x)) before simplification?

• 4x - 3

• (x^2 - 4)^2 - 4

• x^4 - 8x^2 + 12

• x^2 - 4

How many products are formed when multiplying two binomials in g(g(x))?

• Two

• Three

• Five

• Four

What is the final expression for g(g(x)) after simplification?

• x^2 - 4

• 2x - 1

• 4x - 3

• x^4 - 8x^2 + 12

What is the result of multiplying x^2 by x^2 in the process of simplifying g(g(x))?

• x^4

• x^2

• x^3

• x^5

What is the result of combining like terms in the expression for g(g(x))?

• 2x - 1

• 4x - 3

• x^2 - 4

• x^4 - 8x^2 + 12

What is the value of 16 minus 4 in the final expression for g(g(x))?

• 16

• 12

• 10

• 14