InterviewSolution
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InterviewSolution
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Let `f(x)=(x^2-x)/(x^2+2x)` then `d(f^(-1)x)/(dx)` is equal toA. `(-3)/((1-x)^(2))`B. `(3)/((1-x)^(2))`C. `(1)/((1-x)^(2))`D. none of these |
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Answer» Correct Answer - D We have, `f(x)=(x^(2)-x)/(x^(2)+2x)` Clearly, f(x) is not derfined at `x=0, -2` So, Domian `(f)=R-{-2,0}.` For all `x in ` domain (f), we have `f(x)=(x^(2)-x)/(x^(2)+2x)=(x-1)/(x+2)=1-(3)/(x+2)` Now, `fof^(-1)(x)=x` `implies" "f(f^(-1)(x))=x` `implies" "1-(3)/(f^(-1)(x)+2)=x` `implies" "1-x=(3)/(f^(-1)(x)+2)` `implies" "f^(-1)(x)=(3)/(1-x)-2implies(d)/(dx){f^(-1)(x)}=(3)/((1-x)^(2))` |
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