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Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-...

Range of `f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x` is `(pi/4,(3pi)/4)` (b) `[pi/4,(3pi)/4]` `{pi/4,(3pi)/4}` (d) none of these

A

`((pi)/(4), (3pi)/(4))`

B

`[(pi)/(4), (3pi)/(4)]`

C

`{(pi)/(4), (3pi)/(4)}`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) = sin^(-1) x + tan^(-1) x + sec^(-1) x`,
clearly, domain of `f(x) " is " x = +- 1`
Thus, the range is `{f(1), f(-1)}`, i.e., `{(pi)/(4), (3pi)/(4)}`
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