Exercises for Question Type 1: Finding composite functions given two simple functions

Question 1

Skill question

Given $f (x) = 2 x + 5$ and $g (x) = 3 x^{2}$ , find $(f \circ g) (x)$ .

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Question 2

Skill question

Let $f (x) = 2 x + 1$ and $g (x) = x^{2} - 3$ . Find $(f \circ g) (x)$ and state its domain.

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Question 3

Skill question

Let $f (x) = 6 x^{2} + 3$ and $g (x) = x e^{x}$ . Find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 4

Skill question

Let $f (x) = e^{2 x}$ and $g (x) = x^{2}$ . Find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 5

Skill question

Let $f (x) = \frac{3}{x}$ and $g (x) = 1 - x$ . Find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 6

Skill question

Let $f (x) = x$ and $g (x) = x - 4$ . Find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 7

Skill question

Let $f (x) = ln x$ and $g (x) = x^{3}$ . Find $(g \circ f) (x)$ .

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Question 8

Skill question

Let $f (x) = ln (x - 1)$ and $g (x) = e^{x} + 1$ . Find $(f \circ g) (x)$ .

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Question 9

Skill question

Let $f (x) = \frac{1}{x}$ and $g (x) = x + 2$ . Find $(f \circ g) (x)$ .

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Question 10

Skill question

Let $f (x) = \frac{x + 2}{x - 1}$ and $g (x) = 3 x$ . Find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 11

Skill question

Given $f (x) = sin x$ and $g (x) = x^{2}$ , find $(f \circ g) (x)$ and $(g \circ f) (x)$ .

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Question 12

Skill question

Let $f (x) = 3 x$ and $g (x) = x^{2} + 1$ . Find $(f \circ g) (x)$ .

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IB Mathematics Analysis and Approaches Question Type 1: Finding Composite Functions Given Two Simple Functions Exercises