Question

If the function $f\left(x\right)=\{\begin{array}{cc}ax+1,& ifx\le 3\\ bx+3,& ifx>3\end{array}$.is continuous at x = 3 then the relation between a and b is given by

• A. 3(a – b) = 2
• B. 3(a – b) = 1
• C. 3(a – b) = 4
• D. a = b

Answer 1

The correct option is A

3(a – b) = 2

$\underset{x\to 3^{-}}{Lim}f\left(x\right)=\underset{x\to 3^{+}}{Lim}f\left(x\right)\Rightarrow 3x+1=3b+3\Rightarrow 3(a-b)=2$