What vaue of k makes f(x) continous at x=0?

Question

f(x)={k(x²+7) for x>0 5+x for x<0

 

a. 7/5

b. 7

c. 5/7

d. 5

Answer 1

According to exactly what you have typed, 0 is not in the domain of f, so f CANNOT BE CONTINUOUS at 0.

 

However, if k = 5/7, the left and right limits at 0 of f(x) will be the same, so lim (x→0) f(x) will be 5.  BUT THAT DOES NOT MAKE f continuous.

 

(If one of the inequalities on one of the two pieces of the function definition had included the = option, then C would be the answer.)