IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 25
IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Functions, with the answer and a step-by-step solution.
The domain of the real-valued function f\left( x \right) = \frac{\sqrt{x - 1}}{x - 3} is:
- A[1, \infty )
- B[1, 3) \cup (3, \infty )
- C(-\infty , 3) \cup (3, \infty )
- D(1, \infty )
Pick an option, then check.
Answer & solution
Answer: Option B
Two conditions must hold at once.
First, the expression under the square root must not be negative: x − 1 ≥ 0, so x ≥ 1.
Note that x = 1 is allowed, because √0 = 0 is a real number.
Second, the denominator must not be zero: x − 3 ≠ 0, so x ≠ 3.
Combining the two gives all x from 1 upwards except 3.
In interval form that is [1, 3) ∪ (3, ∞).
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