Determine the value(s) of constant(s) involved in the definition so that the given function is continuous: `f(x)={k x+5\ \ \ ,\ \ \ if\ xlt=2x-1\ \ \ ,\ \ \ if\ x >2`

Explanation

`text { At } x=2, f(2)=k(2)+5=2 k+5`




`lim _{x -> 2^{+}} f(x)=lim _{h -> 0} f(2+h) `


`=lim _{h -> 0}[(2+h)-1]=lim _{h -> 0}(1+h)=1`




`lim _{x -> 2^{-}} f(x)=lim _{h -> 0} f(2-h)=lim _{h -> 0}[k(2-h)+5]`


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