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If [a, b] is Range of function f(x) = si...

If [a, b] is Range of function `f(x) = sin^(-1)x + cos^(-1)x + tan^(-1)x` then no. of roots of the equation `1-|x| = tan^(-1)x` is [b] + k then k =

Text Solution

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The correct Answer is:
0
Domain of `sin^(-1)x + cos^(-1) x + tan^(-1) x` is [-1,1]
So range is `[(pi)/(2)-(pi)/(4),(pi)/(2)+(pi)/(4)] = [(pi)/(4),(3pi)/(4)]`
`b = (3pi)/(4)`
`rArr [b] = 2`
Now no. of solution of `1-|x| = tan^(-1)x`
2 solutions.
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