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What is the domain of the function

f(t) = 1/((1 - t)^2 - (1 + t)^2)?

Express your answer in interval notation.

 Jul 30, 2021
 #1
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The domain of the function will be all values of t such that the denominator is non-zero.

 

Find the values of t that make the denominator zero and the domain will be all other values of t:

 

(1-t)2 - (1+t)2 = 0

 

(1-t)2 = (1+t)2

 

Taking the square root of both sides, there are two possibilities:

 

Either:

 

1-t = 1+t

2t = 0

t = 0

 

Or:

 

1-t = -(1+t)

1-t = -1-t

2 = 0

No solution for this case.

 

Therefore the domain of the function is all values of t except t=0.

In interval notation, the domain can be expressed as:

 

(-∞,0) U (0,∞)

 Jul 30, 2021

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