MCQ practice · SSC Higher Mathematics Board questions · Chapter 1: Set and Function
What is the domain of the function f(x) = 2/√(2 − x)?
Think it through first, then pick an option.
- a {x∈ℝ : x < −2}
- b {x∈ℝ : x ≤ −2}
- c {x∈ℝ : x < 2}
- d {x∈ℝ : x ≤ 2}
Answer and explanation
Correct answer: c {x∈ℝ : x < 2}
A root in the denominator needs 2 − x > 0, so x < 2.
Why the other options are wrong
- a {x∈ℝ : x < −2}: Wrong sign: 2 − x > 0 gives x < 2, not x < −2.
- b {x∈ℝ : x ≤ −2}: Wrong sign and an unwanted equals sign; the answer is x < 2.
- d {x∈ℝ : x ≤ 2}: At x = 2 the denominator is √0 = 0, so 2 must be excluded.
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