The given function fis f(x)={ax+1, if x≤3bx+3, if x>3​ If f is continuous at x=3, thenlimx→3​f(x)=limx→33​f(x)=f(3) Also,​x→3lim​f(x)=x→3lim​(ax+1)=3a+1x→3−lim​f(x)=x→3lim​(bx+3)=3b+3f(3)=3a+1​ Therefore, from (1), we obtain​3a+1=3b+3=3a+1⇒3a+1=3b+3⇒3a=3b+2⇒a=b+32​​ Therefore, the required relationship is given by, a=b+32​