Find the values of k so that the function f is continuous at the indicated point in`f(x)={k x+1, ifxlt=5 3x-5, ifx >5`at `x = 5`

Explanation

`f(x) ={{:(kx + 1 "," if x le 5),(3x - 5"," if x gt 5):}`
at x = 5
`f(5) = 5k + 1`
R.H.L. = `underset(x to 5^(+))(lim)f(x)`
Let 5 + h = x
`rArr 5 + h to 5`
`rArr h to 5`
`underset(h to 0 )(lim)f(5 + h)`
`underset(h to 0 )(lim)3(5 + h)-5`
`= 3 (5 + 0) - 5 = 10`
`:'` f(x) is continuous at x =5
` :.` f(5) = R.H.L.
`rArr 5k + 1 = 10 rArr 5k = 9 rArr k= (9)/(5)`