# What is the domain of f(t)=10/(t²-2t-3)?

Sep 28, 2015

The domain is all the real numbers except -1 and 3.

#### Explanation:

$f \left(t\right) = \frac{10}{{t}^{2} - 2 t - 3} \implies$ factor the denominator:
$f \left(t\right) = \frac{10}{\left(t + 1\right) \left(t - 3\right)} \implies$
The domain of a function is all the points where the function is defined, since we can't divide by zero the roots of the denominator are not in the domain, then:
$\left(t + 1\right) \left(t - 3\right) = 0$
$t = - 1 , 3$
Hence the domain is all the real numbers except -1 and 3.
$\left(- \infty , - 1\right) \bigcup \left(- 1 , 3\right) \bigcup \left(3 , \infty\right)$