JEE MAIN - Mathematics (2023 - 13th April Morning Shift - No. 12)
For $$x \in \mathbb{R}$$, two real valued functions $$f(x)$$ and $$g(x)$$ are such that, $$g(x)=\sqrt{x}+1$$ and $$f \circ g(x)=x+3-\sqrt{x}$$. Then $$f(0)$$ is equal to
5
0
$$-$$3
1
Explanation
$$
\begin{aligned}
& g(x)=\sqrt{x}+1 \\\\
& \operatorname{fog}(x)=x+3-\sqrt{x} \\\\
& =(\sqrt{x}+1)^2-3(\sqrt{x}+1)+5 \\\\
& =g^2(x)-3 g(x)+5 \\\\
& \Rightarrow f(x)=x^2-3 x+5 \\\\
& \therefore f(0)=5
\end{aligned}
$$
But, if we consider the domain of the composite function $f \circ g(x)$ then in that case $f(0)$ will be not defined as $\mathrm{g}(\mathrm{x})$ cannot be equal to zero.
But, if we consider the domain of the composite function $f \circ g(x)$ then in that case $f(0)$ will be not defined as $\mathrm{g}(\mathrm{x})$ cannot be equal to zero.
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