Question 1

Which of the following is the correct domain for the function $$f(x) = \sqrt{x - 3} + 1$$?

Accepted Answer

$$x \geq 3$$

Question 2

Given $$f(x) = 3x - 2$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 3

Which of the following statements about the range of $$f(x) = x^2$ - 3x + 7$$ for $$x \in [-2, 4] is $$correct?

Accepted Answer

The range is $$[-7, 5] ($$excluding $$-7$$ and including $$5)$$

Question 4

If $$f(x) = |x^2$ - 3x - 4|$$, which of the following describes how to sketch its graph?

Accepted Answer

Sketch $$y = x^2$ - 3x - 4$$ and reflect the portion below the $$x-$$axis above the $$x-$$axis.

Question 5

Which of the following is NOT a function?

Accepted Answer

$$f: x \mapsto \pm \sqrt{x}$$, \quad x \geq 0$

Question 6

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

Accepted Answer

$$(x + 1)^2$

Question 7

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is f(g(x$$))$$?

Accepted Answer

$$2x^2 + 1$

Question 8

Which of the following best describes the graph of $$y = |x^2$ - 3x|$$?

Accepted Answer

It is the graph of $$y = x^2$ - 3x$$ reflected in the $$x-$$axis for $$y \u003c 0.$$

Question 9

Given $$f(x) = \frac{x+3}{2x-5}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{5x+3}{2x-1}$$

Question 10

A function $$f(x) is $$defined as $$f(x) = \sqrt{x-2}$$ for $$x \geq 2. $$What is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 11

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is g(f(x$$))$$?

Accepted Answer

$$2x^2 + 1$

Question 12

Which of the following is the correct range for the function $$f(x) = \frac{1}{x-1}$$?

Accepted Answer

$$y \in \mathbb{R}, y 
eq 0$$

Question 13

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$f(g(x))$$?

Accepted Answer

$$(x + 2)^2$ - 4$$

Question 14

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Question 15

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is f(g(x$$))$$?

Accepted Answer

$$4x^2 + 4x + 1$

Question 16

Which of the following is the correct range for the function $$f(x) = \sqrt{x^2$ - 4}$$?

Accepted Answer

$$[0, \infty)$$ for $$x \leq -2 or$$ $$x \geq 2$$

Question 17

If $$f(x) = x^2$ - 3x + 4$$ for $$x \leq 3$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 4]$$ for $$x \leq 3$$, but the minimum is at $$x = 1.5$$

Question 18

Which of the following is the correct inverse of $$f(x) = \frac{2x-1}{x+3}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3x+1}{2-x}$$

Question 19

A function $$f(x) is $$defined as $$f(x) = \sqrt{9 - x^2$}$$ for $$x \in [-3, 3]. $$What is the range of $$f(x)$$?

Accepted Answer

$$[0, 3]$$

Pure Mathematics 3 (Edexcel IAL) - Calculus and Functions Study Notes

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