A function f(x) is said to have a removable discontinuity at x=a if:

Question

1. f is either not defined or not continuous at x=a.
2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

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Let
Show that f(x) has a removable discontinuity at x=−7 and determine what value for f(−7) would make f(x) continuous at x=−7.
Must redefine f(−7)=_____________.
Now for fun, try to graph f(x). It's just a couple of parabolas!

Answer 1

f(x) is not given.

As an example, if f(x) is defined as follows:
f(x)=x² for x<0, and
f(x)=2x² for x>0.
Graph f(x) and you will find x=0 is undefined.
Since Lim f(x) x->0- equals Lim f(x) x->0+, we say that there is a removable discontinuity at x=0. The discontinuity can be removed by redefining f(x).

Answer 2

I'm sorry, I was having some problems posting the questions....

Again
Let

f(x)= mx-12 if x is less than -5
x^2 +5x - 7 if x is greater than -5
Show that f(x) has a removable discontinuity at x=−7 and determine what value for f(−7) would make f(x) continuous at x=−7.
Must redefine f(−7)=_____________.

Answer 3

OK I made a mistake... AGAIN fx is not equal to that sorry. I will repost this question.