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# How do I find all points where the following function is discontinuous?

f(x) = 1/(5-(x^2+9)^1/2)((x^2+1)/((1-x)^4))^1/2

Hi Savannah, can you, please, specify the denominator(s) of this function.

5-v(x^2+9) and v(1-x)^4 ... However, I'm a little confused with the second one because it is originally v((x^2+1)/(1-x)^4) ... So I don't know if that counts as a denominator by itself

### 2 Answers by Expert Tutors

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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A function is said to have a point of discontinuity at x = a or the graph of the function has a gap at x = a, if the original function is undefined for x = a, whereas the related rational expression of the function in simplest form is defined for x = a.
... it looks like the denominators are (5 - √(x2 + 9)) and √(1-x)4 then function is undefined if

1. 5 - √(x2 + 9) = 0       or        2. √(1-x)4 = 0
√(x2 + 9) = 5                               x = 1
x2 + 9 = 52
x2 = 16
x = ± 4
The points of discontinuity are {- 4, 1, +4}

Alison O. | Math tutor with 15 years experience - online tutoring availableMath tutor with 15 years experience - on...
4.9 4.9 (133 lesson ratings) (133)
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You want to consider where the denominator will equal zero.

There are two pieces to check.

(1-x) = 0               So, x = 1

5-sqrt(x^2+9)=0   Or, x= +-5

Graphing it can also help.