Question

If $f ( x )= x$ and $g ( x )=| x |$, then $( f + g )( x )$ is equal to

• A. $0$ for all $x \in R$
• B. $2 x$ for all $x \in R$
• C. $ \begin{cases} 2x & \text{for} x \ge 0 \\[2ex] 0, & \text{for} x < 0 \end{cases}$
• D. $ \begin{cases} 0, & \text{for} x \ge 0 \\[2ex] 2x, & \text{for} x < 0 \end{cases}$

Answer 1

Answer: (C)

Given functions are: $f ( x )= x$ and $g ( x )=| x |$
$\therefore (f+g)(x)=f(x)+g(x)=x+\mid x|$
According to definition of modulus function,
$(f + g) (x) = \begin{cases} x + x, & x \ge 0 \\[2ex] x - x, & x < 0 \end{cases} = \begin{cases} 2x, & x \ge 0 \\[2ex] 0, & x < 0 \end{cases}$