First slide

Functions (XII)

Question

If $f : R \to R$ is defined by $f (x) = 2 x + |x|$ , then $f (3 x) - f (- x) - 4 x$ equals

Moderate

A

f(x)
B

-f(x)
C

f(-x)
D

2f(x)

Solution

$f : R \to R$
$f (x) = 2 x + |x| When x \geq 0, then f (x) = 2 x + x = 3 x When x < 0, then f (x) = 2 x - x = x Now, when x \geq 0 f (3 x) - f (- x) - 4 x = 3 (3 x) - (- x) - 4 x = 9 x + x - 4 x = 6 x [∵ x \geq 0] = 2 (3 x) = 2 f (x) [∴ - x \leq 0] When x < 0, f (3 x) - f (- x) - 4 x = 3 x - (- 3 x) - 4 x = 2 x = 2 f (x)$

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