Question

If f R R is defined by f(x)=3x+|x|,then f(2x)-f(-x)-6x is equal to

Answer 1

SOLUTION

GIVEN

f : R → R defined by

$\sf{f(x) = 3x + |x| }$

TO DETERMINE

The value of

$\sf{f(2x) - f( - x) - 6x}$

EVALUATION

Here the given function is

$\sf{f(x) = 3x + |x| }$

Now

$\sf{f(2x) = 3 \times 2x + |2x| = 6x + 2 |x| }$

Again

$\sf{f( - x) = - 3x + | - x| = - 3x + |x| }$

Thus we get

$\sf{f(2x) - f( - x) - 6x}$

$\sf{ = 6x + 2 |x| + 3x - |x| - 6x}$

$\sf{ = 3x + |x| }$

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