Question

Find the relations between $a$ and $b$, so tat the function $f$ defined by:
$f\left(x\right)=\{\begin{array}{c}ax+1,\\ bx+3,\end{array}\begin{array}{c}ifx\le 3\\ ifx>3\end{array}$
is continuous at $x=3$.

Answer 1

Given the function $f\left(x\right)$ is continuous at $x=3$.

Then we'll have,

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

or, $3a+1=3b+3$

or, $3(a-b)=2$.

This is the required relation between $a,b$.