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Sir pls solve the following.

qsnImg
Asked by rsudipto 4th January 2019, 7:15 PM
Answered by Expert
Answer:
begin mathsize 16px style straight x squared straight f open parentheses straight x close parentheses minus 2 straight f open parentheses 1 over straight x close parentheses equals straight g open parentheses straight x close parentheses space..... left parenthesis straight i right parenthesis
Put space 1 over straight x space in space the space above space equation
1 over straight x squared straight f open parentheses 1 over straight x close parentheses minus 2 straight f open parentheses straight x close parentheses equals straight g open parentheses 1 over straight x close parentheses
2 over straight x squared straight f open parentheses 1 over straight x close parentheses minus 4 straight f open parentheses straight x close parentheses equals 2 straight g open parentheses 1 over straight x close parentheses space space space space space space space space space space space space space space space space space space Multiplying space by space 2 space to space get space similar space equation space as space left parenthesis straight i right parenthesis
2 straight f open parentheses 1 over straight x close parentheses minus 4 straight x squared straight f open parentheses straight x close parentheses equals 2 straight x squared straight g open parentheses 1 over straight x close parentheses space space space space space space space space space space space space space left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
straight x squared straight f open parentheses straight x close parentheses minus 2 straight f open parentheses 1 over straight x close parentheses plus 2 straight f open parentheses 1 over straight x close parentheses minus 4 straight x squared straight f open parentheses straight x close parentheses equals straight g open parentheses straight x close parentheses plus 2 straight x squared straight g open parentheses 1 over straight x close parentheses
minus 3 straight x squared straight f open parentheses straight x close parentheses equals straight g open parentheses straight x close parentheses plus 2 straight x squared straight g open parentheses 1 over straight x close parentheses
straight f open parentheses straight x close parentheses equals fraction numerator straight g open parentheses straight x close parentheses plus 2 straight x squared straight g open parentheses 1 over straight x close parentheses over denominator negative 3 straight x squared end fraction
Given space that space straight g left parenthesis straight x right parenthesis space is space odd space function.
straight x squared space is space even space function.
straight f left parenthesis straight x right parenthesis space is space odd.
It space is space given space that space straight f left parenthesis straight x right parenthesis space is space even.
This space contradicts space our space assumption.
Hence comma space straight f left parenthesis straight x right parenthesis equals 0.
straight f left parenthesis 5 right parenthesis equals 0
end style
Answered by Expert 7th January 2019, 9:21 AM
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