1.

If 3f(x)-f((1)/(x))= log_(e) x^(4) for x gt 0 ,then f(e^(x))=

Answer»

X
`log_(e)x `
`e^(x)`
none of these

Solution :We have ,
`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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