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CBSE Class 12-science Answered

Prove that the function f:R-R,given by f(x)=2x,is one-one and onto
Asked by bornalimalakar3 | 05 Oct, 2023, 11:15: AM
answered-by-expert Expert Answer
Given: f(x) = 2x
Let space straight x subscript 1 comma space straight x subscript 2 element of straight R Consider comma space straight f left parenthesis straight x subscript 1 right parenthesis space equals space straight f left parenthesis straight x subscript 2 right parenthesis rightwards double arrow space 2 straight x subscript 1 equals 2 straight x subscript 2 rightwards double arrow space straight x subscript 1 equals straight x subscript 2 Therefore comma space straight f space is space one minus one. Let space straight y equals straight f left parenthesis straight x right parenthesis rightwards double arrow straight y equals 2 straight x rightwards double arrow straight x equals straight y over 2 Since comma space straight y element of straight R space rightwards double arrow space straight y over 2 element of straight R So comma space for space every space straight y space in space the space co minus domain space straight R comma space there space exist space an space element space in space the space domain space such space that space straight f left parenthesis straight x right parenthesis space equals space straight y. Thus comma space straight f space is space onto.
Answered by Renu Varma | 05 Oct, 2023, 11:47: AM

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CBSE 12-science - Maths
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