Q98 / 155 · WBJEE 2020 · Mathematics

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
  • Correct answer
    D
    $\mathrm{S} \cap \mathrm{T}$ is an interval

Solution

Hint: $f(x)=\sqrt{(x-1)(x-2)}, g(x)=\sqrt{x}$ $f(g(x))=\sqrt{(\sqrt{x}-1)(\sqrt{x}-2)}$ $S=\{x: x \in[0,1] \cup[4, \infty)\}$ $g(f(x))=\sqrt{\sqrt{(x-1)(x-2)}}$ $T=\{x: x \in(-\infty, 1] \cup[2, \infty)\}$

Hence, the correct answer is option: 'D'.

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