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Question
if the function
`f(x)=k+x, for x<1`
`=4x+3, for x>=1`
id continuous at x=1 then k=
(a) 7
(b) 8
(c) 6
(d) -6
Solution
(c)
`f(1)=4(1)+3=7`
`lim_(x->1^-)f(x)=lim_(h->0)h(1-h)=lim_(h->0)k+1-h=k+1`
For the function to be continuous at x 1,
`f(1)=lim_(x->1^-)f(x)`
7 = k + 1
k = 6
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