Question

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

Solution

## $$f\left( x \right) =\left\{ \begin{matrix} ax+1,\quad x\le 3 \\ bx+3\quad x>3 \end{matrix} \right. at\ x=3$$function is continuous at $$x=3$$$$LHL=RHL$$$$\displaystyle \lim_{x\rightarrow 3^-}{(ax+1)}=\displaystyle \lim_{x\rightarrow 3^+}{(bx+3)}$$$$a(3)+1=b(3)+3$$$$3a=3b+2$$$$\boxed{a=b+\dfrac23}$$Mathematics

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