What is the domain of the function
f(t) = 1/((1 - t)^2 - (1 + t)^2)?
Express your answer in interval notation.
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,∞)
