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

$ \left\{\begin{array}{ll}0, & \text { for } x \geq 0 \\ 2 x, & \text { for } x < 0\end{array}\right. $

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

f(x)=x

and

g(x)=|x|

, then

(f+g)(x)

is equal to

View answer and explanation

Correct option: C

\left\{\begin{array}{l}2 x, \text { for } x \geq 0 \\ 0, \text { for } x < 0\end{array}\right.

Option C (

\left\{\begin{array}{l}2 x, \text { for } x \geq 0 \\ 0, \text { for } x < 0\end{array}\right.

) is correct because it correctly defines the sum of the functions f(x) = x and g(x) = |x| for all real x.