Let `:[0,pi]rarrR` be defined as
`f(x) ={{:(sinx,"if x is irrational and" x in[0,pi]),(tan^(2)x,"if x is rational and" x in [0,pi]):}`
Then number of points in `[0,pi]` at which the fucntion f is continuous is

Options

A. 6
B. 4
C. 2
D. 0

Answer

B

Explanation

`f(x) ={{:(sinx,x inQ),(tan^(2)x,x in Q):}`
if is continuous at ` x=0,pi`
so 2 points
`sin x=tan^(2)xrArrsinx(cos^(2)x-sinx)=0`
sin x=0
`x=0,pi`
`sin^(2)x+sinx-1= 0`
`sinx-(1+-sqrt(5))/(2)`
`sinx=(sqrt(5)-1)/(2)2` values
Total 4 points