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Which of the following functions are def...

Which of the following functions are defined for all x ?

A

`sin[x]+cos[x] ([x]"denotes the greatest integer " lex)`

B

`sec^(-1)(1+sin^(2)x)`

C

`tan(logx)`

D

`sqrt((9)/(8)+cosx+cos2x)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
(a) Clearly, `sin[x]+cos[x]` is defined for all x.
(b) sin x always defined and `1+sin^(2) x ge 1`
`rArr sec^(-1)(1+sin^(2)x)` is defined for all x, as `1+sin^(2)xge1`
(c) `tan(logx)` is not defined if `logx=(2k+1)(pi)/(2)`
(d) `(9)/(8)+cos x +cos 2x`
`=2cos^(2)x+cosx+(1)/(8)gt0, AAx in R" as "D lt0`
Hence, domain is R.
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