Which of the following functions f has a removable discontinuity at a
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# Which of the following functions f has a removable discontinuity at a

[From: ] [author: ] [Date: 11-09-13] [Hit: ]
and would have a hole at (1,Hoping this helps!......
Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x ≠ a and is continuous at a. (If an answer does not exist, enter DNE.)
f(x)= (x^4 - 1) / (x - 1), a = 1

for g(x) I got (x+1) / (x^2 + 1) but it says the answer is wrong.

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Aremovable discontinuity is a hole, that cancels out. Then you fill it in to remove the discontinuity.

I think you meant to have multiplication where you have the division.

f(x)= (x^4-1)/(x-1)= (x^2-1)(x^2+1)/(x-1)= (x+1)(x-1)(x^2+1)/(x-1)

Now the (x-1) cancels out

So g(x) = (x+1)(x^2+1)= x^3+x^2+x+1, where g(1)= 4

This means f(x) and g(x) are the same except at a=1, where f(x) is undefined, and would have a hole at (1,4)

Hoping this helps!
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