For x R, two real valued functions f(x) and g(x) are such that, g(x)=x+1 and f g(x)=x+3-x.

Question

For $x\in R$, 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

Accepted Answer

$\begin{gathered} g(x)=\sqrt{x}+1 \ fog(x)=x+3-\sqrt{x} \ =(\sqrt{x}+1{)}^{2}-3(\sqrt{x}+1)+5 \ ={g}^{2}(x)-3g(x)+5 \ \Rightarrow f(x)={x}^{2}-3x+5 \ 	herefore f(0)=5 \end{gathered}$

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 $g(x)$ cannot be equal to zero.

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