The value of b for which the function

(a) $-1$

Given: $f(x)$ is continuous at every point of its domain. So, it is continuous at $x=1$.

$\Rightarrow \lim _{x \rightarrow 1^{+}} f(x)=f(1)$

$\Rightarrow \lim _{h \rightarrow 0} f(1+h)=f(1)$

$\Rightarrow \lim _{h \rightarrow 0}\left(4(1+h)^{2}+3 b(1+h)\right)=5(1)-4$

$\Rightarrow 4+3 b=1$

$\Rightarrow-3=3 b$

$\Rightarrow b=-1$