InterviewSolution
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InterviewSolution
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Find the values of x for which the following pair of functions are identical. (i) `f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x` (ii) `f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)` |
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Answer» (i) `f(x)=tan^(-1)x+cot^(-1)x ,x in R.` ` " and " g(x)=sin^(-1)x +cos^(-1)x=(pi)/(2) " for " x in [-1,1]` Hence functions are identical if ` x in [-1,1].` (ii) `f(x)=cos(cos^(-1)x)` is defined if `cos^(-1)x` is defined for which ` x in [-1,1].` ` g(x)=cos^(-1)(cosx)` is defined if `cosx in [-1,1],` which is true `AA x in R.` So, domain is R. Thus, common domain of two functions is `[-1,1].` ` :. f(x) =x " and " g(x) =x " for " [-1,1].` |
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