Composite Functions

Math ⇒ Functions

Composite Functions starts at 11 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Composite Functions. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

Given f(x) = √x and g(x) = x - 1, what is the domain of (f ∘ g)(x)?

Given f(x) = 2x - 1 and g(x) = x^2, what is (g ∘ f)(2)?

Given f(x) = x - 1 and g(x) = 3x, find (g ∘ f)(2).

Given f(x) = x + 2 and g(x) = 5x, what is (g ∘ f)(x)?

Given f(x) = x^2 - 1 and g(x) = x + 3, what is (f ∘ g)(x)?

Given f(x) = x^2 + 1 and g(x) = x - 2, find (g ∘ f)(1).

Given f(x) = x^2 and g(x) = 2x, what is (f ∘ g)(-3)?

Given f(x) = x^2 and g(x) = x - 4, find (f ∘ g)(5).

If f(x) = √x and g(x) = x + 4, what is the domain of (f ∘ g)(x)?

If f(x) = 1/(x-1) and g(x) = x^2, for which value(s) of x is (f ∘ g)(x) undefined?

Given f(x) = 2x and g(x) = x^2, which of the following is (g ∘ f)(x)? (1) 2x^2 (2) (2x)^2 (3) x^2 + 2x (4) 2x + x^2

Which of the following is the correct definition of a composite function? (1) f(g(x)) (2) g(f(x)) (3) f(x) + g(x) (4) f(x) × g(x)

Which of the following is the correct order for evaluating (f ∘ g)(x)? (1) Apply f first, then g (2) Apply g first, then f

Fill in the blank: The composite function (f ∘ g)(x) is defined as f(______).

Fill in the blank: The composition (f ∘ g)(x) is only defined when the output of g(x) is in the ______ of f(x).

Fill in the blank: The range of (f ∘ g)(x) depends on the ______ of g(x) and the range of f(x).

If f(x) = 2x and g(x) = x^2, is (f ∘ g)(x) equal to (g ∘ f)(x)?

If f(x) = x^2 and g(x) = √x, is (f ∘ g)(x) defined for all real numbers?

True or False: (f ∘ g)(x) is always equal to (g ∘ f)(x).

True or False: The composition of two functions is always a function.