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Which of the following functions is non-...

Which of the following functions is non-periodic? (1) `2^x/2^[x]=` (2) `sin^(-1)({x})` (3) `sin^(-1)(sqrt(cosx))` (4) `sin^(-1)(cos x^2)`

A

f(x) = tan (3x+5)

B

g(x)={x}, the fractional part of x

C

`f(x)=1-(cos^(2)x)/(1+tanx)-(sin^(2))/(1+cotx)`

D

`phi(x)=x+ cos x `

Text Solution

Verified by Experts

The correct Answer is:
D
We observe that
`f(x)=tan(3x+5)` is periodic with period `(pi)/(3)`
`g(x)={x}=x-[x]` has period 1
`h(x)=1-(cos^(3)x+ sin^(3)x)/(cosx+ sinx)`
`implies h(x)=1-(cos^(2)x+sin^(2)x-sinx cosx)`
`implies h(x)=(1)/(2) sin 2x` has period `pi`. and , `phi(x)=x+cosx` is non- periodic, because x is non- periodic.
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