Composite Functions
Math ⇒ Functions
Composite Functions starts at 11 and continues till grade 12.
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See sample questions for grade 12
Given f(x) = 2x + 1 and g(x) = 3x - 2, find x such that (f ∘ g)(x) = 7.
Given f(x) = 2x + 1 and g(x) = x^2, find all x such that (g ∘ f)(x) = 9.
Given f(x) = 2x + 3 and g(x) = x - 5, find (f ∘ g)(x) and (g ∘ f)(x).
Given f(x) = 3x and g(x) = x^2, find (f ∘ g)(-2).
Given f(x) = x^2 - 1 and g(x) = x + 2, find (g ∘ f)(x).
Given h(x) = 3x - 1 and k(x) = x + 4, what is (h ∘ k)(2)?
If f(x) = √x and g(x) = x - 1, what is the domain of (f ∘ g)(x)?
If f(x) = 1/(x-1) and g(x) = x^2, for which values of x is (f ∘ g)(x) undefined?
If f(x) = 1/x and g(x) = x - 2, find the domain of (f ∘ g)(x).
Given f(x) = x^2 and g(x) = 2x + 3, which of the following is (f ∘ g)(x)?
(1) (2x + 3)^2
(2) 2x^2 + 3
(3) x^2 + 2x + 3
(4) 2(x^2) + 3
If f(x) = x^2 and g(x) = 2x, which of the following is (g ∘ f)(x)?
(1) 2x^2
(2) (2x)^2
(3) 2(x^2)
(4) x^2 + 2x
Which of the following is the correct definition of the composite function (f ∘ g)(x)?
(1) f(g(x))
(2) g(f(x))
(3) f(x) + g(x)
(4) f(x) - g(x)
Let f(x) = |x| and g(x) = x - 3. Which of the following is (f ∘ g)(x)?
(1) |x| - 3
(2) |x - 3|
(3) |x| + 3
(4) |x + 3|
Fill in the blank: If f(x) = x^2 and g(x) = x + 1, then (f ∘ g)(x) = _____
Fill in the blank: The composite function (f ∘ g)(x) is defined only when x is in the domain of _____ and g(x) is in the domain of _____.
Fill in the blank: The process of finding a function h such that h(x) = (f ∘ g)(x) is called _____ of functions.
If f(x) = x + 1 and g(x) = 2x, 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) = (g ∘ f)(x) for all functions f and g.
True or False: If f and g are both one-to-one functions, then (f ∘ g) is also one-to-one.
