WBJEE · Maths · Functions
Let \(\mathrm{f}(\mathrm{x})=\sqrt{\mathrm{x}^{2}-3 \mathrm{x}+2}\) and \(\mathrm{g}(\mathrm{x})=\sqrt{\mathrm{x}}\) be two given functions. If \(\mathrm{S}\) be the domain of \(\mathrm{f} \circ \mathrm{g}\) and \(\mathrm{T}\) be the domain of \(\mathrm{g}\) of then
- A \(S=T\)
- B \(S \cap T=\phi\)
- C \(\mathrm{S} \cap \mathrm{T}\) is a singleton
- D \(\mathrm{S} \cap \mathrm{T}\) is an interval
Answer & Solution
Correct Answer
(D) \(\mathrm{S} \cap \mathrm{T}\) is an interval
Step-by-step Solution
Detailed explanation
Hint: \(f(x)=\sqrt{(x-1)(x-2)}, g(x)=\sqrt{x}\) \(f(g(x))=\sqrt{(\sqrt{x}-1)(\sqrt{x}-2)}\) \(S=\{x: x \in[0,1] \cup[4, \infty)\}\) \(g(f(x))=\sqrt{\sqrt{(x-1)(x-2)}}\) \(T=\{x: x \in(-\infty, 1] \cup[2, \infty)\}\)
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