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If $\mathrm{f}(\mathrm{x})=\mathrm{x}$ and $\mathrm{g}(\mathrm{x})=|\mathrm{x}|$, then what is $(\mathrm{f}+\mathrm{g})(\mathrm{x})$
equal to ?
Options:
equal to ?
Solution:
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Verified Answer
The correct answer is:
$\left\{\begin{array}{l}2 \mathrm{x}, \text { for } \mathrm{x} \geq 0 \\ 0, \text { for } \mathrm{x} < 0\end{array}\right.$
Given functions are : $\mathrm{f}(\mathrm{x})=\mathrm{x}$ and $\mathrm{g}(\mathrm{x})=|\mathrm{x}|$
$\therefore \quad(\mathrm{f}+\mathrm{g})(\mathrm{x})=\mathrm{f}(\mathrm{x})+\mathrm{g}(\mathrm{x})=\mathrm{x}+|\mathrm{x}|$
According to defintion of modulus function,
$(f+g)(x)=\left\{\begin{array}{ll}x+x, & x \geq 0 \\ x-x, & x < 0\end{array}\right.$
$=\left\{\begin{array}{cl}2 \mathrm{x}, & \mathrm{x} \geq 0 \\ 0, & \mathrm{x} < 0\end{array}\right.$
$\therefore \quad(\mathrm{f}+\mathrm{g})(\mathrm{x})=\mathrm{f}(\mathrm{x})+\mathrm{g}(\mathrm{x})=\mathrm{x}+|\mathrm{x}|$
According to defintion of modulus function,
$(f+g)(x)=\left\{\begin{array}{ll}x+x, & x \geq 0 \\ x-x, & x < 0\end{array}\right.$
$=\left\{\begin{array}{cl}2 \mathrm{x}, & \mathrm{x} \geq 0 \\ 0, & \mathrm{x} < 0\end{array}\right.$
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