Question

Given a function $f\left(x\right)=\{\begin{array}{ccc}-1& if& x\le 0\\ ax+b& if& 0<x<1\\ 1& if& x\ge 1\end{array}$ where $a,b$ are constants. The function is continuous everywhere.

What is the value of $b$?

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $-1$

$\underset{x\to 0}{lim}f\left(x\right)=\underset{x\to 0}{lim}(-1)=-1$

$\underset{x\to 0^{-}}{lim}f\left(x\right)=\underset{x\to 0^{-}}{lim}(ax+b)=a\left(0\right)+b=b$

Given it is continuous

$f(-1)=$LHL$\Rightarrow -1=b$