Find the value of the constant `k` so that the given function is continuous at the indicated point: `f(x)={k x+1,\ \ \ if\ xlt=5 3x-5,\ \ \ if\ x >5` at `x=5`

Explanation

The given function f is continuous at `x=5`,

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


`lim​_(x→5−)f(x)=lim​_(x→5+)f(x)=f(5)`

`⇒lim​_(x→5)(kx+1)`


`=lim​_(x→5)(3x−5)=5k+1`

`⇒5k+1=15−5=5k+1`

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