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f:R->R is defined as f(x)=2x+|x| then f(...

`f:R->R` is defined as `f(x)=2x+|x|` then `f(3x)-f(-x)-4x=`

A

a) `f(x)`

B

b) `-f(x)`

C

c) `f(-x)`

D

d) `2f(x)`

Text Solution

Verified by Experts

The correct Answer is:
D
`f : R rarr R`
`f(x) = 2x + |x|`
When `x ge 0`, then f(x) = 2x + x = 3x
When `x lt 0`, then f(x) = 2x - x = x
Now, when `x ge 0`
`f(3x)-f(-x)-4x=3x-(-3x)-4x=2x=2f(x)`
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