InterviewSolution
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InterviewSolution
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Which of the following pairs of function/functions has same graph?`y=tan(cos^(-1)x); y=(sqrt(1-x^2))/x``y=t a n(cot^(-1)x);y=1/x``y="sin"(tan^(-1)x); y=x/(sqrt(1-x^2))``y="cos"(tan^(-1)x); y=s in(cot^(-1)x)`A. `y = tan (cos^(-1) x), y = (sqrt(1 - x^(2)))/(x)`B. `y = tan (cot^(-1) x), y = (1)/(x)`C. `y = sin (tan^(-1) x), y = (x)/(sqrt(1 + x^(2)))`D. `y = cos (tan^(-1) x), y = sin (cot^(-1) x)` |
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Answer» Correct Answer - A::B::C::D (1) `y = tan (cos^(-1)x) and y = (sqrt(1 -x^(2)))/(x)` or `y = tan (tan^(-1).(sqrt(1 -x^(2)))/(x)) = (sqrt(1 -x^(2)))/(x) and y = (sqrt(1 -x^(2)))/(x)` `:. D_(1) = [-1, 1] - {0} and D_(2) = [-1, 1] {0}` So functions are identical and hence they have same graph (2) `y = tan (cot^(-1) x) and y = (1)/(x)` `:. y = tan (tan^(-1).(1)/(x)) adn y = (1)/(x)` or `y = (1)/(x) adn y = (1)/(x)` `:. D_(1) = R - {0} and D_(2) = R - {0}` So, functions are identical and hence they have same graph (3) `y = sin (tan^(-1) x) and y = (x)/(sqrt(1 + x^(2)))` or `y = sin (sin^(-1).(x)/(sqrt(1 + x^(2)))) = (x)/(sqrt(1 + x^(2))) and y = (x)/(sqrt(1 + x^(2)))` or `D_(1) = R, D_(2) = R` So, functions are identical and hence they have same graph. (4) `y = cos (tan^(-1) x) and y = sin (cot^(-1) x)` or `y = cos (tan^(-1) x) = cos [cos^(-1).(1)/(sqrt(1 + x^(2)))] = (1)/(sqrt(1 + x^(2)))` and `y = sin (cot^(-1) x) = sin (sin^(-1).(1)/(sqrt(1 + x^(2)))) = (1)/(sqrt(1 + x^(2)))` `:. D_(1) = R and D_(2) = R` So, functions are identical and hence they have same graph. |
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