The greatest value assumed by the function f(x) = 5 - $| x - 3 |$ is

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Solution

The correct option is D 5
f(x) = $5 - | x - 3 |$
When, $x \geq 3$
f(x) = $5 - x + 3 = 8 - x$
Thus, maximum value will be when x is least. $x = 3$
Hence, f(x) = $5$
When, $x < 3$
f(x) = $5 + x - 3$ = $2 + x$
Thus, f(x) is maximum when x is maximum, or $x = 3$
Hence, f(x) = $5$
Thus, maximum value of the function is $5$

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