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Find the value of K, if f(x) = kx +1 if ...

Find the value of K, if f(x) = kx +1 if `x<=5` ; 3x-5 if x >5 is continuous at x=5.

Text Solution

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`lim_(h->0)f(x-h)=f(x)=lim_(h->0)f(x+h)`
RHL
`=lim_(h->0)f(x+h)=lim_(h->0)3(x+h)-5=3x+3h=5`
`=3*5-5=10`
`f(5)=10`
`5k+1=10`
`5k=9`
`k=9/5`.
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