First slide

Functions (XII)

Question

If f : R → R, g : R → R be two given functions then f (x) = 2 min { f (x) – g (x), 0} equals

Moderate

A

f (x) + g (x) – |g (x) – f (x)|
B

f (x) + g (x) + |g (x) – f (x)|
C

f (x) – g (x) + |g (x) – f (x)|
D

f (x) – g (x) – |g (x) – f (x)|

Solution

We have, f (x) = 2 min { f (x) – g (x), 0}
$= \{\begin{array}{lr} 0 f (x) > g (x) \\ 2 [f (x) - g (x)], f (x) \leq g (x) \end{array} = \{\begin{cases} f (x) - g (x) - | f (x) - g (x) |, f (x) > g (x) \\ f (x) - g (x) - | f (x) - g (x) |, f (x) \leq g (x) \end{cases}$
$∴$ f (x) = f (x) – g (x) –|g (x) – f (x)|

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