Question
Download Solution PDFThe domain of the function \(y = \frac{x}{\sqrt{x^2 - 3x + 2}}\) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
1. Function y = √x is defined for x ≥ 0
2. Polynomial y = p/q is defined for q ≠ 0
Calculation:
Given that,
\(y = \frac{x}{\sqrt{x^2 - 3x + 2}}\)
As discussed above, y is defined for
x2 - 3x + 2 > 0
⇒ (x - 2)(x - 1) > 0
This represents, a product of the two-term is positive, which can be possible in two cases.
Case:1 (x - 2) and (x - 1), both positive
⇒ x > 2 or x ϵ (2, ∞) ----(1)
Case:2 (x - 2) and (x - 1), both negative
⇒ x < 1 or x ϵ (-∞, 1) ----(2)
Hence, from (1) & (2)
⇒ x ϵ (-∞, 1) ∪ (2, ∞)
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