Suppose `f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db`are positive inte – InterviewSolution

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1.	Suppose `f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db`are positive integers. If `f(g(20))-g(f(20))=28 ,`then which of the following is nottrue?`a=15`b. `a=6`c. `b=14`d. `b=3`A. `a=15`B. `a=6`C. `b=14`D. `b=3`
Answer» Correct Answer - D `f(g(x))=a(bx+a)+b` `=abx+a^(2)+b" (i)"` `g(f(x))=b(ax+b)+a` `=abx+b^(2)+a" (ii)"` From (i) - (ii), we get `f(g(20))-g(f(20))=a^(2)-b^(2)+b-a` `therefore" "(a^(2)-b^(2))+(b-a)=28` `therefore" "(a-b)(a+b-1)=28=1xx 2x or 2 xx 14 or 4xx7` If `a-b=1 and a+b-1=28` Then `a=15, b=14` If `a-b=2 and a+b-1=14` (not possible) If `a-b=4 and a+b-1 =7` Then a = 6 and b = 2

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