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CBSE Class 11-commerce Answered

L e t space f equals left curly bracket left square bracket x comma fraction numerator x squared over denominator 1 plus x squared end fraction right square bracket colon x element of R right curly bracket space b e space a space f u n c t i o n space f r o m space R space i n t o space R. space D e t e r m i n e space t h e space r a n g e space o f space f.
Asked by kanhagupta2003 | 31 Jul, 2019, 09:12: AM
answered-by-expert Expert Answer
begin mathsize 16px style Here comma straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x squared over denominator 1 space plus space straight x squared end fraction Let space straight f left parenthesis straight x right parenthesis space equals space straight y rightwards double arrow fraction numerator straight x squared over denominator 1 space plus space straight x squared end fraction space equals space straight y rightwards double arrow straight x squared space equals space straight x squared straight y space plus space straight y rightwards double arrow straight x squared open parentheses 1 space minus space straight y close parentheses equals straight y rightwards double arrow straight x space equals space plus-or-minus square root of fraction numerator straight y over denominator 1 minus space straight y end fraction end root Clearly space straight x space will space take space real space value space if space fraction numerator straight y over denominator 1 minus space straight y end fraction space greater or equal than space 0 rightwards double arrow fraction numerator straight y over denominator space straight y space minus space 1 end fraction space less or equal than space 0 rightwards double arrow 0 space less or equal than space straight y space less than space 1 rightwards double arrow straight y space element of left square bracket 0 comma space 1 right parenthesis Hence space comma space Range space of space straight f space equals space left square bracket 0 comma space 1 right parenthesis end style
Answered by Yasmeen Khan | 31 Jul, 2019, 03:48: PM

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