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

Explanation

`f`(3) = 3u + 1
R.H.L. = ` underset (x to 3^(+))(lim)f(x)`
`=underset (h to 0)(lim) f(3+h)`
`=underset (h to 0)(lim) b(3 + h)+= 3b+3`
L.H.L. = ` underset (x to 3^(-))(lim)f(x)`
`=underset (h to 0)(lim) f(3-h)`
`=underset (h to 0)(lim) a(3 + h)+1= 3a+1`
`:'` Function ia continuous at x = 3
`rArrr 3a + 1 = 3b + 3 `
`rArr ` 3a = 3b + 2 and b` ne` R