Question

$f\left(x\right)\begin{array}{c}=2,forx<1\\ =ax+b,for1\le x<3\\ =3,forx\ge 3\end{array}$ is continuous at $x=1$ and $x=3$, find $a$ and $b$.

Answer 1

$f\left(x\right)$ is continious at $x=1$

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

$\Rightarrow 2=a+b...\left(i\right)$

$f\left(x\right)$ is continious at $x=3$

$\underset{x\to 3}{lim}f\left(x\right)=f\left(3\right)$

$\Rightarrow 3a+b=3...\left(ii\right)$

Solving (i) & (ii) $a=\frac{1}{2},b=\frac{3}{2}$