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**+6 **

Multiply out the denominator and combine like terms:

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

(x^{2} - 2x + 1) + (x^{2} + 2x + 1)

x^{2} - 2x + 1 + x^{2} + 2x + 1

2x^{2} + 2

Now set this equal to 0 and solve for x.

2x^{2} + 2 = 0

2x^{2} = -2

x^{2} = -1

x = i

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

( - ∞, ∞)

hectictar
Mar 12, 2017