Functions and Inverse Functions Practice Questions
Matric (South Africa) · Matric Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
42
Easy
74
Medium
29
Hard
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Sample Questions from Functions and Inverse Functions
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Q1
Easy
What is the value of f(3) if the function f(x) = 2x + 1?
A.
7
B.
6
C.
8
D.
5
Show Answer & Explanation
Correct Answer: A
To find f(3), substitute 3 into the function: f(3) = 2(3) + 1 = 6 + 1 = 7.
Q2
Easy
Which of the following represents the inverse of the function f(x) = 3x + 2?
A.
f⁻¹(x) = (x - 2)/3
B.
f⁻¹(x) = 3(x - 2)
C.
f⁻¹(x) = (x + 2)/3
D.
f⁻¹(x) = 3x + 2
Show Answer & Explanation
Correct Answer: A
To find the inverse, swap x and y: x = 3y + 2, then solve for y to get y = (x - 2)/3, hence f⁻¹(x) = (x - 2)/3.
Q3
Easy
If f(x) = 2x + 3, what is the value of f(4)?
A.
11
B.
8
C.
7
D.
5
Show Answer & Explanation
Correct Answer: A
To find f(4), substitute x with 4 in the function. f(4) = 2(4) + 3 = 8 + 3 = 11.
Q4
Medium
What is the inverse of the function f(x) = 3x + 5?
A.
f^(-1)(y) = (y - 5)/3
B.
f^(-1)(y) = 3y + 5
C.
f^(-1)(y) = (y + 5)/3
D.
f^(-1)(y) = (y - 3)/5
Show Answer & Explanation
Correct Answer: A
To find the inverse, set y = 3x + 5 and solve for x. Rearranging gives x = (y - 5)/3, hence the inverse is f^(-1)(y) = (y - 5)/3.
Q5
Medium
If f(x) = x^2 - 4, find f^(-1)(x).
A.
f^(-1)(x) = √(x + 4)
B.
f^(-1)(x) = -√(x + 4)
C.
f^(-1)(x) = ±√(x + 4)
D.
f^(-1)(x) = √(x - 4)
Show Answer & Explanation
Correct Answer: C
The function f(x) = x^2 - 4 is a quadratic function and its inverse can have both positive and negative roots. Thus, f^(-1)(x) = ±√(x + 4).
Q6
Medium
Determine the value of x if f(x) = 2x - 1 and its inverse is equal to f(3).
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
Show Answer & Explanation
Correct Answer: A
First, find f(3) = 2(3) - 1 = 5. The inverse function f^(-1)(x) = (x + 1)/2. Setting this equal to 5 gives x = 4.
Q7
Medium
Which of the following is a property of inverse functions?
A.
f(f^(-1)(x)) = x for all x in the domain of f^(-1)
B.
f(x) = f^(-1)(x) for all x.
C.
The graph of f and f^(-1) are always the same.
D.
The range of f is equal to the domain of f^(-1).
Show Answer & Explanation
Correct Answer: A
A fundamental property of inverse functions is that applying the function and then its inverse returns the original value: f(f^(-1)(x)) = x.
Q8
Hard
Given the function f(x) = 3x^2 - 12x + 7, what is the inverse of the function f, if it exists?
A.
f^(-1)(x) = 2 - sqrt(x - 7)/3
B.
f^(-1)(x) = sqrt((x - 7)/3) + 4
C.
f^(-1)(x) = (x + 12)/3
D.
f^(-1)(x) = sqrt((x - 7)/3) - 4
Show Answer & Explanation
Correct Answer: D
To find the inverse function, we need to express x in terms of y. Rearranging the original function leads to an equation where we can isolate y. Solving gives us the correct inverse as f^(-1)(x) = sqrt((x - 7)/3) - 4.
Q9
Hard
Given the function f(x) = 2x^2 - 8x + 5, what is the inverse function f^-1(x) if it exists?
A.
f^-1(x) = √(x + 4) + 4
B.
f^-1(x) = x/2 + 4
C.
f^-1(x) = 4 - √(x - 5)/2
D.
f^-1(x) = x^2 + 4x - 5
Show Answer & Explanation
Correct Answer: C
To find the inverse, we first need to express y = 2x^2 - 8x + 5, then solve for x in terms of y. Rearranging gives x = 4 - √((y - 5)/2), thus f^-1(x) = 4 - √(x - 5)/2.
Q10
Hard
If the function f(x) = 2x^2 - 4x + 1 is given, what is the equation of its inverse function?
A.
f^-1(x) = x^2 + 2x + 1
B.
f^-1(x) = x/2 + 2
C.
f^-1(x) = sqrt((x + 4)/2)
D.
f^-1(x) = x^2 - 2x + 1
Show Answer & Explanation
Correct Answer: C
To find the inverse function, we first set y = 2x^2 - 4x + 1 and then solve for x in terms of y. After rearranging, we find x = (sqrt((y + 4)/2)) and thus f^-1(x) = sqrt((x + 4)/2).
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Functions and Inverse Functions — Matric (South Africa) Matric Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Functions and Inverse Functions in Matric (South Africa) Matric Mathematics. The questions are organized by difficulty — 42 easy, 74 medium, 29 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.