NCERT Solutions for Class 11-science Maths Chapter 2 - Relations and Functions

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Chapter 2 - Relations and Functions Ex. 2.1

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Chapter 2 - Relations and Functions Ex. 2.2

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Chapter 2 - Relations and Functions Ex. 2.3

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Chapter 2 - Relations and Functions Misc. Ex.

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Given colon space straight f open parentheses straight x close parentheses equals fraction numerator straight x squared over denominator 1 plus straight x squared end fraction
Let space straight y equals fraction numerator straight x squared over denominator 1 plus straight x squared end fraction
rightwards double arrow straight y plus yx squared equals straight x squared
rightwards double arrow straight y equals straight x squared minus yx squared
rightwards double arrow straight y equals straight x squared open parentheses 1 minus straight y close parentheses
rightwards double arrow fraction numerator straight y over denominator 1 minus straight y end fraction equals straight x squared
rightwards double arrow straight x equals square root of fraction numerator straight y over denominator 1 minus straight y end fraction end root
straight x space is space defined space only space if space fraction numerator straight y over denominator 1 minus straight y end fraction greater or equal than 0
rightwards double arrow straight y greater or equal than 0 space and space 1 minus straight y greater or equal than 0
rightwards double arrow straight y greater or equal than 0 space and space 1 greater or equal than straight y
straight y not equal to 1
Therefore comma space straight y greater or equal than 0 space and space 1 greater than straight y
rightwards double arrow 0 less or equal than straight y less than 1
rightwards double arrow straight y element of left square bracket 0 comma space 1 right parenthesis
rightwards double arrow fraction numerator straight x squared over denominator 1 plus straight x squared end fraction element of left square bracket 0 comma space 1 right parenthesis
Hence comma space the space range space of space straight f space is space left square bracket 0 comma space 1 right parenthesis.

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