Explanation:
the domain is the interval or set of all valid values for the input variable (here t).
so, what is not included there is every input value that is not valid for the function.
f(t) = 20/(2t - 21)
so, we have a fraction here.
in what case is a fraction invalid or undefined ?
well, when the denominator (the bottom) is 0.
because a division by 0 is invalid or undefined.
so, we must avoid that the denominator of f(t) becomes 0, ever.
and that means we have to forbid (exclude from the domain) any value for t that turns the denominator 0.
is there such a value ?
let's see :
2t - 21 = 0
2t = 21
t = 21/2 = 10.5
aha !
yes, such a value exists : 10.5
and therefore we must exclude t = 10.5 from the domain of the function.