1.

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)`

Answer» Correct Answer - 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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