A) 0 for all \[x\in R\]
B) 2x for all \[x\in R\]
C) \[\left\{ \begin{matrix} 2x,for\,\,x\ge 0 \\ 0,for\,\,x<0 \\ \end{matrix} \right.\]
D) \[\left\{ \begin{matrix} 0,for\,\,x\ge 0 \\ 2x,for\,\,x<0 \\ \end{matrix} \right.\]
Correct Answer: C
Solution :
[c] Given functions are: \[f(x)=x\] and \[g(x)=\left| x \right|\] \[\therefore (f+g)(x)=f(x)+g(x)=x+\left| x \right|\] According to definition of modulus function, \[(f+g)(x)=\left\{ \begin{matrix} x+x,\,\,x\ge 0 \\ x-x,\,\,x<0 \\ \end{matrix}=\left\{ \begin{matrix} 2x,\,\,x\ge 0 \\ 0,\,\,x<0 \\ \end{matrix} \right. \right.\]
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