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

Answer 1

(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