Answer 1

The given function f  `f(x) = {(kx + 1, "," if x <= 5),(3x - 5, "," if x > 5):}`

The given function f is continuous at x = 5, if f is defined at x = 5 and if the value of fat x = 5 equals the limit of f at x = 5

It is evident that f is defined at x = 5 and `f(x ) = kx + 1 = 5k + 1`

Therefore, the required value of k is `9/5`