suppose g(x)= (1/x+1 if x<1 and 2x-1if x>/1. The best description concerning the continuity of g(x) is that the function:

Question

A. has a jump discontinuity

B. has both jump and infinite discontinuity

C. has a removable discontinuity

D. is continuos

E. has an infinite discontinuity

Answer 1

g(x) = 1/x + 1 for x < 1 and g(x) = 2x-1 for x ≥ 1

has a jump discontinuity at x = 1 since the limit as x --> 1 from below for g(x) = 2, and g(x)=1 for x=1.

It also has an infinite discontinuity at x =0.

So, the answer is B).