Question

Express a in terms of b if the function f defined by $f\left(x\right)=\left\{\begin{array}{cc}ax+1& ,x\le 3\\ bx+3& x>3\end{array}\right\}$ is continuous at $x=3$.

Answer 1

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

function is continuous at $x=3$

$LHL=RHL$

$\underset{x\to 3^{-}}{lim}(ax+1)=\underset{x\to 3^{+}}{lim}(bx+3)$

$a\left(3\right)+1=b\left(3\right)+3$

$3a=3b+2$

$a=b+\frac{2}{3}$