Question

Find the value of k that makes the following function continuous.

f (x) = x^2 -k , if x < -1
2x-1, if x is equal to greater than -1

How would I do this algebraically?

Answer 1

wats the value of f(x) when x = -1 ?

Answer 2

Aha! I found it.

Being a quadratic function for x<-1 and a linear one for x>-1, f(x) is continuous on these 2 intervals. Now, it has to be continuous for x=-1 as well, To be continuous, lim for x-->-1 with x<-1 must be equal to lim for x-->-1 with x>-1 and equal to f(-1).

lim for x-->-1 with x<-1 = (-1)^2-k = 1-k
lim for x-->-1 with x>-1 = 2(-1)-1 = -3
f(-1) = 2(-1)-1 = -3

Therefore, 1-k = -3 so k=4

Answer 3

good job !