Let $f(x)=\sqrt{x^{2}-3 x+2}$ and $g(x)=\sqrt{x}$ be two given functions. If $S$ be the domain of $f \circ g$ and $T$ be the domain of $g \circ f$, then

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Let $f(x)=\sqrt{x^{2}-3 x+2}$ and $g(x)=\sqrt{x}$ be two given functions. If $S$ be the domain of $f \circ g$ and $T$ be the domain of $g \circ f$, then

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kritika · Answer 1 · 2021-12-26T19:30:21+0000

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

Let \(f(x)=\sqrt{x^{2}-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of \(f \circ g\) and \(T\) be the domain of \(g \circ f\), then

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