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SIR PL TELL THE BELOW QUESTION FROM ATTACHED IMAGE

Asked by neeraj.unnao 30th January 2017, 5:48 PM
Answered by Expert
Answer:
begin mathsize 16px style Given space that space straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x minus 3 over denominator 2 straight x plus 1 end fraction
Domain space of space straight f colon space Clearly comma space straight f left parenthesis straight x right parenthesis space is space defined space for space all space straight x element of straight R space except space for space which space
2 straight x plus 1 equals 0 comma space that space is space straight x equals negative 1 half
Hence comma space domain space of space straight f equals straight R minus open curly brackets negative 1 half close curly brackets
Range space of space straight f colon space Let space straight f left parenthesis straight x right parenthesis space equals space straight y
rightwards double arrow space fraction numerator straight x minus 3 over denominator 2 straight x plus 1 end fraction equals straight y
rightwards double arrow straight x minus 3 equals straight y left parenthesis 2 straight x plus 1 right parenthesis
rightwards double arrow straight x minus 3 equals 2 xy plus straight y
rightwards double arrow straight x minus 2 xy equals straight y plus 3
rightwards double arrow straight x left parenthesis 1 minus 2 straight y right parenthesis equals straight y plus 3
rightwards double arrow straight x equals fraction numerator straight y plus 3 over denominator 1 minus 2 straight y end fraction
Clearly comma space straight x space will space take space real space values space for space all space straight x element of straight R space except space for space
1 minus 2 straight y equals 0
rightwards double arrow straight y equals 1 half
So comma space range space left parenthesis straight f right parenthesis space equals space straight R minus open curly brackets 1 half close curly brackets. end style
Answered by Expert 31st January 2017, 8:02 AM
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