Question

If $f(x)=\left\{\begin{array}{ll}1, & x \leq 3 \\ a x+b, & 3<x<5 \\ 7, & 5 \leq x\end{array}\right.$ is continuous, then $(a, b)$ are given by

(a) $(3,8)$

(b) $(-3,-8)$

(c) $(2,-8)$

(d) $(3,-8)$

Answer 1

SOLUTION —  At $x=3$,

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

and at $x=5,5 a+b=7$

$\begin{array}{ll}\Rightarrow & a=3 \\\text { and } & b=-8\end{array}$

So, The correct option of this question will be (C).