InterviewSolution
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InterviewSolution
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If `f(x)=x(x-1)`is a function from `[1/2,oo)to[-1/4,oo),`then `{x in r :f^(-1)(x)=f(x)}`isa. null setb. `{0,2}`c. `{2}`d. a set containing 3 elementsA. null setB. `{0,2}`C. `{2}`D. a set containing 3 elements |
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Answer» Correct Answer - C `{x in R:f^(-1)(x)=f(x)}` `={x in R:(f(x))=x}` `f(f(x))=f(x(x-1))=[x(x-1)][x(x-1)-1]` `=x(x-1)[x^(2)-x-1]` Now, `f(f(x))=x` `rArr" "x(x-1)(x^(2)-x-1)=x` `rArr" "x(x^(3)-2x^(2))=0` `rArr" "x=2 (because x in [(1)/(2),oo))` |
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