If f(x)=3x−4, then f⁻¹(5) equals:
- 1
- 3
- 5
- 11
Show answer and explanation
Answer: B. 3
Solve 3x−4=5 ⇒ x=3.
FSC Mathematics: Functions and Limits, questions with answers
Practise 31 real Federal Board questions on Functions and Limits from 2023 to 2026. See the answer and explanation as soon as you answer.
31real questions
11multiple choice
5exam sessions
About Functions and Limits in FSC Mathematics
Functions and Limits is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th and 12th class), and about 6% of its real questions come from it. Tayyari Karo has 31 real questions on this chapter from 2023 to 2026; 11 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 19 medium, 8 easy, 4 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
If f(x)=√(x+1) for x≥−1, then the range of f⁻¹(x) is:
- (−∞,0]
- [0,∞)
- (−∞,−1]
- [−1,∞)
Show answer and explanation
Answer: D. [−1,∞)
Range of f⁻¹ = domain of f = [−1,∞).
lim x→∞ (1+3/x)^(x/3) =
- 0
- 1
- e
- 1/e
Show answer and explanation
Answer: C. e
Let t=x/3: (1+1/t)^t → e as t→∞.
If lim x→1 f(x)=4 and lim x→1 g(x)=0, then lim x→1 f(x)/g(x) results:
- 0
- Does not exist
- 1
- 4
Show answer and explanation
Answer: B. Does not exist
Numerator→4≠0 while denominator→0 ⇒ limit does not exist (unbounded).
Without finding the inverse, what is the range of f⁻¹(x), where f(x)=3+√(x−2)?
- [2,∞)
- [3,∞)
- [0,∞)
- [−2,∞)
Show answer and explanation
Answer: A. [2,∞)
Range of f⁻¹ = Domain of f. Since f requires x−2≥0, Domain of f = [2,∞).
If f(x) = x² + 1 and g(x) = x − 1, then g(f(x)) =
- x²
- x² − 1
- x² + 1
- x² − 2
Show answer and explanation
Answer: A. x²
g(f(x)) = f(x) − 1 = (x²+1) − 1 = x².
If f(x)=(2x−3)/(x+1), find f⁻¹(x). Also determine the domain and range of f⁻¹(x).
Show model answer
y(x+1)=2x−3 ⇒ x(y−2)=−(y+3) ⇒ x=(y+3)/(2−y)
f⁻¹(x) = (x+3)/(2−x)
Domain of f⁻¹ = ℝ\{2}; Range of f⁻¹ = ℝ\{−1}
Evaluate lim x→0 [x sin4x/(1−cos2x)]
Show model answer
As x→0: sin4x≈4x, 1−cos2x≈2x²
Expression ≈ x(4x)/(2x²) = 4x²/2x²
= 2
Sessions with Functions and Limits questions
| Session | Questions |
|---|---|
| 2026 Annual | 6 |
| 2025 1st Annual | 6 |
| 2025 2nd Annual | 6 |
| 2024 Annual | 7 |
| 2023 Annual | 6 |
Common questions
What does the Functions and Limits chapter cover on this page?
31 real Federal Board (FBISE) Mathematics questions on Functions and Limits from 2023 to 2026, for 11th and 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Integration 39
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17