Find the values of *k *so that the function *f* is continuous at the indicated point.

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

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#### Solution

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 *f*at *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`

Concept: Algebra of Continuous Functions

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