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For \mathrm{x \in R}, two real valued functions \mathrm{f(x) \: and \: g(x)} are such that, \mathrm{g(x)=\sqrt{x}+1} and fog \mathrm{(x)=x+3-\sqrt{x}}. Then \mathrm{f(0)} is equal to

 

Option: 1

5
 


Option: 2

0


Option: 3

-3
 


Option: 4

1


Answers (1)

best_answer

\begin{aligned} & g(x)=\sqrt{x}+1 \\ \end{aligned}

\begin{aligned} & \text { fog }(x)=x+3-\sqrt{x} \\ \end{aligned}

\begin{aligned} & =(\sqrt{x}+1)^2-3(\sqrt{x}+1)+5 \\ \end{aligned}

\begin{aligned} & =g^2(x)-3 g(x)+5 \\ \end{aligned}

\begin{aligned} & \Rightarrow f(x)=x^2-3 x+5 \\ \end{aligned}

\begin{aligned} & \therefore f(0)=5 \end{aligned}
But, if we consider the domain of the composite function \mathrm{fog (x)} then in that case \mathrm{f(0)} will be not defined as \mathrm{\mathrm{g}(\mathrm{x})} cannot be equal to zero.

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HARSH KANKARIA

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