Consider the following statements:
1. The function f(x)=[x] where [.] is the greatest integer function defined on R, is continuous at all points except at x=0.
2. The function `f(x)=sin|x|` is continuous for all `x""inR`.
Which of the above statements is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

B

Explanation

The greatest integer function is continuous at all statement points except integer. Hence, statement 1 is incorrect.
Statement 2 : Let `h(a)=sinxandg(x)=|x|`
`hog(x)=sin|x|`
`impliesf(x)=hog(x)=sin|x|`
Therefore, g(x) is continuous, `AAx""inRandh(x)` is continuous `AAx""inR`
When both are continuous then hog(x) is also continuous.
Thus, statement 2 is correct.