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The set of all x for which $f (x) = \log_{\frac{x - 2}{x + 3}} 2$ and $g (x) = \frac{1}{\sqrt{x^{2} - 9}}$ are both not defined is

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(– 3, 2)

[– 3, 2)

(– 3, 2]

[–3, 2]

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detailed solution

Correct option is D

The function f is not defined for - 3 ≤ x ≤ 2 and g is not defined for those x for which x2 - 9 ≤0 i.e., x ∈ [– 3, 3]. Thus f and g are not defined on [-3, 2].

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The set of all x for which f(x)=logx−2x+3⁡2 and g(x)=1x2−9 are both not defined is

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The set of all x for which $f (x) = \log_{\frac{x - 2}{x + 3}} 2$ and $g (x) = \frac{1}{\sqrt{x^{2} - 9}}$ are both not defined is