Given a function
`f(x)={{:(-1,If,xle0),(ax+b,If,0ltxlt1),(1,If,xge1):}`
where a, b are constants. The function is continuous everywhere.
What is the value of b?

Options

A. `-1`
B. 1
C. 0
D. 2

Answer

A

Explanation

`F(x)={{:(-1",",xle0),(ax+b",",0ltxlt1),(1",",xge1):}`
At x=0,
`L.H.L=R.H.L`
`underset(xto0^(-))limf(x)=underset(xto0^(+))limf(x)`
`-1=underset(xto0)lim(ax+b)`
-1=b
Since the given function is also continuous at x=1
`L.H.L=R.H.L`
`underset(xto1^(-))limf(x)=underset(xto1^(+))limf(x)`
a+b=1
a-1=1
a=1+1=2.
From solution 82, b=-1.