The maximum value of $f (x) = - | log (x - 3) | + 3$ is

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Solution

Graph of $y = log x$ is

Now shift this curve towards right by $3$ units
$\Rightarrow y = log (x - 3)$

Now, graph of $y = | log (x - 3) |$ is

We get $y = - | log (x - 3) |$ by inverting the graph of $y = | log (x - 3) |$ with respect to $x -$ axis.

For $y = - | log (x - 3) | + 3,$ we move the curve upwards by $3$ units.

Hence, the maximum value is $3.$

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m

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