• Best of luck to the class of 2020 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Looking for HSC notes and resources?
    Check out our Notes & Resources page

any suggestions about how to approach this question on continuous pdf? (1 Viewer)

Fizsi

New Member
Joined
Aug 29, 2014
Messages
3
Gender
Female
HSC
N/A
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?
 

cossine

New Member
Joined
Jul 24, 2020
Messages
19
Gender
Male
HSC
2017
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.
 

CM_Tutor

Well-Known Member
Joined
Mar 11, 2004
Messages
1,448
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:

.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top