Calculus
posted by Abigail .
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!

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). 
I'm sorry, I was having some problems posting the questions....
Again
Let
f(x)= mx12 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)=_____________. 
OK I made a mistake... AGAIN fx is not equal to that sorry. I will repost this question.
Respond to this Question
Similar Questions

calculus please help!
Which of the following functions f has a removable discontinuity at a? 
Calculus
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 f(x)=2x^2+3x–14/x–2 … 
Calculus
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 f(x)=2x^2+3x–14/x–2 … 
calculus
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 f(x)= x2+10x+26 … 
Calculus
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.  … 
Calculus
Suppose g(x) = { 1 / (x  2) if x < 1 2x  4 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontinuity C.) has an infinite discontinuity D.) has a removable … 
Calculus  #2
Suppose g(x)={x^2+2x+1/x+1 if x<1 {2x if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. … 
Calculus  #3
Suppose g(x)={1/(x2) if x<1 {2x3 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. … 
Calculus  #4
Suppose g(x)={1/(x2) if x<1 {2x4 if x≥1 The best description concerning the continuity of g(x) is that the function: is continuous. has a jump discontinuity. has an infinite discontinuity. has a removable discontinuity. … 
CalculusHelp Please
Find a function f(x), perhaps a piecewise function that is defined but not continuous on (infinity, infinity) for which the function lf(x)l is both defined and continuous on (infinity, infinity). f(x)= lf(x)l =