Creating Functions through Composition

What is the main focus of the video?

• Solving linear equations

• Defining function composition expressions

• Graphing functions

• Evaluating functions at a point

In the composition f(g(x)), what is g(x) considered as?

• The output of f(x)

• The input to f(x)

• A constant value

• An independent variable

What do we replace x with in the function f(x) when composing f(g(x))?

• x^2

• g(x)

• 1 + x

• f(x)

What is the simplified form of f(g(x)) given g(x) = x / (1 + x)?

• 1 / (x + 1)

• sqrt((x / (1 + x))^2 - 1)

• sqrt(x^2 - 1)

• x^2 / (1 + x^2)

What is the result of f(g(x)) if g(x) = x / (1 + x) and f(x) = sqrt(x^2 - 1)?

• sqrt(x^2 - 1)

• 1 / (x + 1)

• x^2 / (1 + x^2)

• sqrt((x / (1 + x))^2 - 1)

In the composition g(f(x)), what is f(x) considered as?

• An independent variable

• A constant value

• The input to g(x)

• The output of g(x)

What do we replace x with in the function g(x) when composing g(f(x))?

• 1 + x

• x^2

• g(x)

• f(x)

What is the simplified form of g(f(x)) given f(x) = sqrt(x^2 - 1)?

• sqrt(x^2 - 1)

• sqrt((x / (1 + x))^2 - 1)

• sqrt(x^2 - 1) / (1 + sqrt(x^2 - 1))

• 1 / (x + 1)

Are the compositions f(g(x)) and g(f(x)) generally the same?

• No, unless the functions are linear

• Yes, they are always the same

• No, they are generally different

• Yes, if x is a constant

What is the result of g(f(x)) if f(x) = sqrt(x^2 - 1) and g(x) = x / (1 + x)?

• 1 / (x + 1)

• sqrt((x / (1 + x))^2 - 1)

• sqrt(x^2 - 1)

• sqrt(x^2 - 1) / (1 + sqrt(x^2 - 1))