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If 3f(x)-f((1)/(x))= log_(e) x^(4) for x gt 0 ,then f(e^(x))= |
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Answer» X `3f(x)-F((1)/(x))=log_(e) x^(4)` `implies 3f(x)-f((1)/(x))=4 log_(e)x "" ` ….(i) `implies 3f((1)/(x))-f(x)=4 log_(e)((1)/(x))""`[Replacing x by 1/x] `implies 3f((1)/(x))-f(x)=-4 log_(e)x""`…..(ii) Solving (i) and (ii) , we get `8f(x)=8log_(e)x implies f(x)=log_(e)ximplies f(e^(x))=x` |
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