Question
Download Solution PDFThe domain of the function f : R → R defined by \(\rm \sqrt {x^2 \ - \ x - 110}\) is.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The domain of a function is the complete set of possible values of the independent variable.
To find domain of √f(x), set f(x) ≥ o
Calculations:
Given: the function f : R → R defined by \(\rm \sqrt {x^2 \ - \ x - 110}\)
We know that the domain of a function is the complete set of possible values of the independent variable.
To find the domain
= x2 - x - 110 ≥ 0
= x2 - 11x + 10x - 110 ≥ 0
= x(x - 11) + 10(x - 11) ≥ 0
= (x + 10)(x - 11) ≥ 0
= x ≤ - 10 or x ≥ 11
= x ∈ (- ∞, - 10] ∪ [11, ∞)
Hence, the domain of the function f : R → R defined by f(x) = \(\rm \sqrt {x^2 \ - \ x - 110}\) is (- ∞, - 10] ∪ [11, ∞)
Last updated on May 31, 2025
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