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  4. If f(x)=3-x,-4 le x le 4, then the domain of log e (f (x)) is

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Q. If $ f(x)=3-x,-4\le x\le 4, $ then the domain of $ {{\log }_{e}}\,(f\,(x)) $ is

J & K CETJ & K CET 2011Relations and Functions

Solution:

Given, $ f(x)=3-x,\,\,-4\le x\le 4 $
Now, $ {{\log }_{e}}\,f\{(x)\}=lo{{g}_{e}}\,(3-x) $
Here, existance for the above function $ 3-x>0 $
$ \Rightarrow $ $ x-3<0 $
$ \Rightarrow $ $ x<3 $
So, the domain of $ {{\log }_{e}}\,\{f\,(x)\,\} $ is $ (-\infty ,\,3). $