Question

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

Answer 1

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

Explanation:

`f(t)=10/(t^2-2t-3)=>` factor the denominator:
`f(t)=10/[(t+1)(t-3)]=>`
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:
`(t+1)(t-3)=0`
`t=-1,3`
Hence the domain is all the real numbers except -1 and 3.
`(-oo,-1)uuu(-1,3)uuu(3,oo)`