InterviewSolution
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InterviewSolution
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`f(x)=x^2-2a x+a(a+1),f:[a ,oo)vec[a ,oo)dot`If one of the solution of the equation `f(x)=f^(-1)(x)i s5049 ,`then the other may be5051 (b) 5048 (c)5052 (d) 5050A. 5051B. 5048C. 5052D. 5050 |
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Answer» Correct Answer - B::D `f(x)=x^(2)-2ax+a(a+1)` ` f(x)=(x-a)^(2)+a, x in [a,oo)` Let `y=(x-a)^(2)+a. " Clearly " y ge a.` Thus, `(x-a)^(2)=y-a` `or x=a+sqrt(y-a)` ` :. f^(-1)(x)=a+sqrt(x-a)` Now, ` f(x) =f^(-1)(x)` `or (x-a)^(2)+a=a+sqrt(x-a)` `(x-a)^(2) =sqrt(x-a)` ` or (x-a)^(4)=(x-a)` i.e., `x= a or (x-a)^(3) =1` i.e., ` x=a or a+1 ` If ` a=5049, " then " a+1=5050.` If `a+1=5049, " then " a=5048.` |
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