+4609 What is the domain of the function \(f(t) = \frac{1}{(t-1)^2+(t+1)^2}~?\)Express your answer in interval notation
+9465 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.
( - ∞, ∞)
