Q.1 Which of the following is an example of a function?
y² = x
x² + y² = 1
y = 2x + 3
x² + y = 5
Explanation - A function relates each input to exactly one output. The equation y = 2x + 3 defines a unique y for every x, so it is a function.
Correct answer is: y = 2x + 3
Q.2 The domain of f(x) = 1/x is:
All real numbers
All real numbers except 0
Positive real numbers
Only integers
Explanation - The function f(x) = 1/x is undefined at x = 0, so its domain is all real numbers except 0.
Correct answer is: All real numbers except 0
Q.3 If f(x) = x², then f(–3) equals:
–9
9
0
–6
Explanation - Substituting x = –3 gives f(–3) = (–3)² = 9.
Correct answer is: 9
Q.4 Which of the following is NOT a function?
y = x + 1
y = √x
y² = x
y = |x|
Explanation - The equation y² = x gives two possible values of y (positive and negative) for one value of x, so it is not a function.
Correct answer is: y² = x
Q.5 If f(x) = 2x + 5, what is f(0)?
2
5
10
–5
Explanation - f(0) = 2(0) + 5 = 5.
Correct answer is: 5
Q.6 The range of f(x) = x² is:
All real numbers
x ≥ 0
x ≤ 0
Integers only
Explanation - Since a square is never negative, the range of x² is all non-negative real numbers.
Correct answer is: x ≥ 0
Q.7 What is the limit of (x² – 1)/(x – 1) as x → 1?
0
1
2
Does not exist
Explanation - Factoring numerator: (x² – 1) = (x – 1)(x + 1). Cancelling gives x + 1. At x = 1, value = 2.
Correct answer is: 2
Q.8 Which function is constant?
f(x) = 3
f(x) = x
f(x) = x²
f(x) = 1/x
Explanation - A constant function assigns the same value for all x, which is true for f(x) = 3.
Correct answer is: f(x) = 3
Q.9 The function f(x) = |x| is:
Odd
Even
Neither
Both
Explanation - Since f(–x) = |–x| = |x| = f(x), the function is even.
Correct answer is: Even
Q.10 If f(x) = √x, then the domain is:
All real numbers
x > 0
x ≥ 0
Only integers
Explanation - Square root is defined only for non-negative numbers, so domain is x ≥ 0.
Correct answer is: x ≥ 0
Q.11 What is lim (x → 0) sin x / x?
0
1
∞
Does not exist
Explanation - The standard limit result is lim (x → 0) sin x / x = 1.
Correct answer is: 1
Q.12 If f(x) = 1/x, then f(–2) = ?
–2
–1/2
2
1/–2
Explanation - f(–2) = 1/(–2) = –1/2.
Correct answer is: –1/2
Q.13 The function f(x) = x³ is:
Odd
Even
Neither
Constant
Explanation - Since f(–x) = (–x)³ = –x³ = –f(x), the function is odd.
Correct answer is: Odd
Q.14 The domain of f(x) = 1/√x is:
x > 0
x ≥ 0
All real numbers
x ≠ 0
Explanation - Since denominator cannot be zero and square root requires non-negative input, domain is x > 0.
Correct answer is: x > 0
Q.15 If f(x) = 2x and g(x) = x + 1, then (f ∘ g)(x) = ?
2x + 1
2x + 2
x² + 1
2x²
Explanation - (f ∘ g)(x) = f(g(x)) = f(x + 1) = 2(x + 1) = 2x + 2.
Correct answer is: 2x + 2
Q.16 What is lim (x → ∞) 1/x?
0
1
∞
Does not exist
Explanation - As x becomes very large, 1/x approaches 0.
Correct answer is: 0
Q.17 If f(x) = x² – 4, then f(2) = ?
0
–4
4
8
Explanation - f(2) = (2)² – 4 = 4 – 4 = 0.
Correct answer is: 0
Q.18 The range of f(x) = cos x is:
(–∞, ∞)
[–1, 1]
[0, ∞)
Integers only
Explanation - Cosine function varies between –1 and 1 inclusive.
Correct answer is: [–1, 1]
Q.19 Which function is not defined for x = 0?
f(x) = x²
f(x) = sin x
f(x) = 1/x
f(x) = |x|
Explanation - 1/0 is undefined, so f(x) = 1/x is not defined at x = 0.
Correct answer is: f(x) = 1/x
Q.20 What is lim (x → 0) (1 – cos x)/x²?
0
1/2
1
Does not exist
Explanation - Standard limit identity: lim (x → 0) (1 – cos x)/x² = 1/2.
Correct answer is: 1/2
Q.21 If f(x) = x + 2, then f(–5) = ?
–3
–7
7
3
Explanation - f(–5) = –5 + 2 = –3.
Correct answer is: –3
Q.22 The function f(x) = ln x has domain:
x > 0
All real numbers
x ≥ 0
x ≠ 0
Explanation - Logarithm is defined only for positive real numbers.
Correct answer is: x > 0
Q.23 If f(x) = e^x, then f(0) = ?
0
1
e
∞
Explanation - f(0) = e⁰ = 1.
Correct answer is: 1
Q.24 Which of the following functions is bounded?
f(x) = x²
f(x) = sin x
f(x) = e^x
f(x) = ln x
Explanation - Sine function oscillates between –1 and 1, hence it is bounded.
Correct answer is: f(x) = sin x
Q.25 What is lim (x → 0⁺) ln x?
∞
0
–∞
Does not exist
Explanation - As x approaches 0 from the right, ln x tends to negative infinity.
Correct answer is: –∞