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if the function f(x)=k+x,for x<1, =4x+3,for x≥1 id continuous at x=1 then k= - Mathematics and Statistics

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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

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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

 

Concept: Definition of Continuity - Continuity of a Function at a Point
  Is there an error in this question or solution?

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