InterviewSolution
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InterviewSolution
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Domain (D) and range (R) of `f(x)=sin^(-1)(cos^(-1)[x]),`where [.] denotes the greatest integer function, is`D-=x in [1,2],R in {0}`D`-=x in 90 ,1],R-={-1,0,1}``-=x in [-1,1],R-={0,sin^(-1)(pi/2),sin^(-1)(pi)}``-=x in [-1,1],R-={-pi/2,0,pi/2}`A. `[1, 2) and {0}`B. `[0, 1] and {-1, 0, 1}`C. `[-1, 1] and {0, sin ^(-1)((pi)/(2)),sin^(-1) (pi)}`D. `[-1 1] and {- (pi)/(2), 0, (pi)/(2)}` |
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Answer» Correct Answer - A Let `f(x) = cos^(-1)[x] and g(x) = sin^(-1) x`. Then, `phi(x) = gof(x)`. Clearly `D(f) = [-1,1), R(f) = [Cos^(-1)(-1), cos^(-1) (0), cos^(-1)(1)]= {pi,(pi)/(2),0}` `D(g) = [-1,1] and R(g) =[-(pi)/(2),(pi)/(2)]` `therefore" "D(phi) = D(gof) = {x : x in D(f) and f(x) in D(g)}` `={x: x in [-1,2) and f(x)in [-1,1]}` `{x:x in {-1,2) and cos^(-1) [x] in [-1,1]}` `=[1,2)` `R(phi) ={ phi (x) : x in |1,2)}= { sin^(-1) (cos^(-1)1)}={sin^(-1)(0)} = {0}` |
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