F Fizsi New Member Joined Aug 29, 2014 Messages 2 Gender Female HSC N/A Sep 15, 2020 #1 A piecewise function f(x) is defined as follows f(x)=-x+a ,x<0 f(x)= 1/x+a, x greater or equal to 0 What value or values of a make the function continous?

A piecewise function f(x) is defined as follows f(x)=-x+a ,x<0 f(x)= 1/x+a, x greater or equal to 0 What value or values of a make the function continous?

C cossine New Member Joined Jul 24, 2020 Messages 16 Gender Male HSC 2017 Sep 15, 2020 #2 lim x->0^+ (1/x + a) = infinity lim x-> 0^- (-x+a) = a Therefore there is no value of "a" that makes the function continuous as the left and right one-sided limits are different.

lim x->0^+ (1/x + a) = infinity lim x-> 0^- (-x+a) = a Therefore there is no value of "a" that makes the function continuous as the left and right one-sided limits are different.

C CM_Tutor Well-Known Member Joined Mar 11, 2004 Messages 1,446 Sep 27, 2020 #3 I think that @Fizsi means the piece of the function for to be rather than because, as @cossine has noted, this second interpretation leads to no solution being possible. Assuming the first interpretation, for , we have and for , we have For to be continuous, the branches must meet and the limits must be the same, and thus: .

I think that @Fizsi means the piece of the function for to be rather than because, as @cossine has noted, this second interpretation leads to no solution being possible. Assuming the first interpretation, for , we have and for , we have For to be continuous, the branches must meet and the limits must be the same, and thus: .