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CBSE Class 12-science Answered

 Show that function f in A = R – {2/3} defined as f(x) = 4x+3/6x-4 is one-one and onto. Hence find f-1 mention each and every formula and minute details
Asked by haroonrashidgkp | 07 Jun, 2018, 10:56: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals fraction numerator 4 straight x plus 3 over denominator 6 straight x minus 3 end fraction
straight f left parenthesis straight a right parenthesis equals straight f left parenthesis straight b right parenthesis
fraction numerator begin display style 4 straight a plus 3 end style over denominator begin display style 6 straight a minus 3 end style end fraction equals fraction numerator begin display style 4 straight b plus 3 end style over denominator begin display style 6 straight b minus 3 end style end fraction
24 ab minus 12 straight a plus 18 straight b minus 9 equals 24 ab plus 18 straight a minus 12 straight b minus 9
straight a equals straight b
One space one

straight y equals fraction numerator begin display style 4 straight x plus 3 end style over denominator begin display style 6 straight x minus 3 end style end fraction
straight x equals fraction numerator 3 plus 3 straight y over denominator 6 straight y minus 4 end fraction equals straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis
straight f left parenthesis fraction numerator begin display style 3 plus 3 straight y end style over denominator begin display style 6 straight y minus 4 end style end fraction right parenthesis equals fraction numerator begin display style 4 open parentheses fraction numerator begin display style 3 plus 3 straight y end style over denominator begin display style 6 straight y minus 4 end style end fraction close parentheses plus 3 end style over denominator begin display style 6 open parentheses fraction numerator begin display style 3 plus 3 straight y end style over denominator begin display style 6 straight y minus 4 end style end fraction close parentheses minus 3 end style end fraction equals straight y
ONTO


end style
Answered by Arun | 08 Jun, 2018, 10:49: AM
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