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What is the domain of the function \(f(t) = \frac{1}{(t-1)^2+(t+1)^2}~?\)Express your answer in interval notation

tertre  Mar 12, 2017
 #1
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Multiply out the denominator and combine like terms:

(x - 1)(x - 1) + (x + 1)(x + 1)

(x2 - 2x + 1) + (x2 + 2x + 1)

x2 - 2x + 1 + x2 + 2x + 1

2x2  + 2

 

Now set this equal to 0 and solve for x.

2x2 + 2 = 0

2x2 = -2

x2 = -1

x = i

 

There are no real numbers that make the y undefined. So the domain is all real numbers.

( - ∞, ∞)

hectictar  Mar 12, 2017

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