Posted by **Abigail** on Sunday, February 6, 2011 at 12:47am.

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

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.

--------------------------------------------------------------------------------

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!

- Calculus-incomplete -
**MathMate**, Sunday, February 6, 2011 at 7:59am
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).

- Calculus -
**Abigail**, Monday, February 7, 2011 at 12:29pm
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)=_____________.

- Calculus -
**Abigail**, Monday, February 7, 2011 at 12:46pm
OK I made a mistake... AGAIN fx is not equal to that sorry. I will repost this question.

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