Question

Find the values of $a$ and $b$ so that the function $f\left(x\right)=$$\left\{\begin{array}{c}3ax+b,ifx\ge 1\\ 11,ifx=1\\ 5ax-2b,ifx<1\end{array}\right\}$ continuous at $x=1$.

Answer 1

$f\left(x\right)=\{\begin{array}{c}3ax+b\\ 11\\ 5ax-2b\end{array}\begin{array}{c}x\ge 1\\ x=1\\ x<\end{array}$

$Atx=1:f\left(x\right)$ is continuous

$LHL=RHL=11$

$3a+b=11---\left(1\right)$

$5a-2b=11---\left(2\right)$

on solving we get

$a=3,b=2$