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Grade 12IIT JEE Entrance Exam

2f( x^2 ) + 3f( 1 / x^2 ) = x^2 -1 for all x belongs to R-{0} THEN find F(x)
please i really want to master these type of questions.

Profile image of Ravinder Singh
11 Years agoGrade 12
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1 Answer

Profile image of Kamal Saab
ApprovedApproved Tutor Answer11 Years ago
Take x^2=X (hence X belongs to (0, infinity) )
 
Now,
2f(X) + 3f(1/X) = X – 1 ------------------- (1)
2f(1/X) + 3f(X) = 1/X – 1 -----------------(2)
 
Two equation... Two variables (i.e. f(X) and f(1/X)), eliminate f(1/X) and get f(X).
take X=x and get f(x).
Cheers!

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