Find the relationship between a and b so that the function f defined by`f(x)={{:(a x+1, ifxlt=3),(b x+3,ifx >3):}` is continuous at `x = 3`.

Explanation

Taking the LHL at x=3,


`lim_(xrarr3^-)f(x)=lim_(hrarr0)f(3-h)=lim_(hrarr0)a(3-h)+1=3a+1`


RHL at x=3,


`lim_(xrarr3^+)f(x)=lim_(hrarr0)f(3+h)=lim_(hrarr0)b(3+h)+3=3b+3`


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