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If f(x) = sin^(-1) (sin ("log"(2) x)), t...

If `f(x) = sin^(-1) (sin ("log"_(2) x))`, then find the value of `f(300)`

Text Solution

Verified by Experts

The correct Answer is:
`3 pi - "log"_(2) 300`
`f(300) = sin^(-1) (sin (log._(2) 300))`
`log_(2) 256 = 8 and log_(2) 512 = 9`
`:. (log_(2) 300) in (8,9)`
`:. Sin^(-1) (sin (log_(2) 300) = sin^(-1) (sin (3pi - log_(2) 300))`
`= 3pi - log_(2) 300`
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