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Q.

If f:R→R is defined by f(x)=2x+x, then f3x-f-x-4x equals

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a

f(x)

b

-f(x)

c

f(-x)

d

2f(x)

answer is D.

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Detailed Solution

f:R→R                               f(x)=2x+x When x≥0,then  f(x)=2x+x=3x When x<0, then f(x)=2x-x=x Now, when x≥0 f(3x)-f(-x)-4x=33x--x-4x=9x+x-4x                                =6x                                ∵x≥0                                 =23x=2fx              ∴-x≤0 When x<0, f(3x)-f(-x)-4x=3x--3x-4x=2x=2f(x)
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