Function Domains and Composite Functions

The video tutorial by Amal Kumar covers composite functions, including their domain, range, and transformations. It presents three main questions, each focusing on different aspects of composite functions, such as graphing, transformations, and inverse functions. The tutorial also includes a test question to reinforce understanding. Key concepts like domain restrictions and the influence of inside functions on composite functions are explained in detail.

What is the main focus of the video tutorial?

• Introduction to algebraic expressions

• Basics of calculus

• Review of composite functions

• Understanding linear equations

How is a composite function generally represented?

• f(x) * g(x)

• f(g(x))

• f(x) - g(x)

• f(x) + g(x)

What is the domain of the function f(x) = 1/(x + 12)?

• All real numbers except x = -12

• All real numbers except x = 12

• All real numbers

• All real numbers except x = 0

What is the range of the function g(x) = 2x^2 + 4?

• All real numbers less than 4

• All real numbers

• All real numbers greater than or equal to 4

• All real numbers except 0

What is the result of f(g(1)) if f(x) = 1/(x + 12) and g(x) = 2x^2 + 4?

• 1/14

• 1/18

• 1/20

• 1/16

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

• All real numbers

• All real numbers greater than 4

• All real numbers except x = -12

• All real numbers except x = 0

How is the graph of f(g(x)) = 2x^2 - 1 described?

• Vertical stretch by a factor of 2 and translation 1 unit down

• Horizontal stretch by a factor of 2 and translation 1 unit up

• Vertical stretch by a factor of 3 and translation 2 units down

• Horizontal stretch by a factor of 3 and translation 2 units up

What is the inverse of the function f(x) = 1/(x - 2)?

• 1/(x + 2)

• 1/(x - 2)

• 1 + 2x

• 1/(x + 1)

What is the domain of the function f(x) = √x?

• x < 0

• x ≤ 0

• x ≥ 0

• x > 0

What is the domain of the function g(x) = √(4 - x)?

• x ≤ 4

• x < 4

• x ≥ 4

• x > 4