Let `f(x)=[x]`, where [.] is the greatest integer function and `g(x)=sinx` be two real valued functions over R.
Which of the following statements is correct?

Options

A. Both f(x) and g(x) are continuous at x=0
B. f(x) is continuous at x=0, but g(x) is not continuous at x=0.
C. g(x) is continuous at x=0, but f(x) is not continuous at x=0.
D. Both f(x) and g(x) are discontinuous at x=0.

Answer

C

Explanation

`f(x)=[x]andg(x)=sinx`
`underset(xto0^(+))limf(x)=[0+h]=0`
`underset(xto0^(-))limf(x)=[0-h]=-1`
f(0)-0
`impliesf(x)` is not continuous at x=0 and also g(x) is continuous at x=0. (every trignometric function is continuous).