Question

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

Answer 1

Given $f\left(x\right)=\{\begin{array}{c}ax+1ifx\le 3\\ bx+3ifx>3\end{array}$

Given function is continious at x=3

When ${lim}_{x\to 3}l\left(x\right)=l\left(3\right)$

$\Rightarrow 3b+3=3a+1$

$\Rightarrow 3a-3b=2$

$\Rightarrow a-b=\frac{2}{3}$

$\therefore a-b=\frac{2}{3}$