1. Finding the Domain

Find the domain of the following functions:

1) h(x)= 1/ 4sqrt(x^2-5x)
2) f(t)= t^2 - 6t
3) H(t)= (4-t^2)/ (2-t)

Any help would be appreciated.

2. For the 1st problem when the radical in denominator is not 0 or less than 0

For the 3rd problem factor the the numerator

3. [1-]
becuase its under radical then it might be (x^2 - 5x >= 0) and because its in denominator then i(x^2 - 5x > 0).

Now we solve this inequality. To solve it we finds the roots of this inequality. To find the roots we set it
(x^2 - 5x = 0) => and we finds roots (x1 = 0)(x2 = 5) and now we find the sign through a scatterpoint and after that we realize that x>5 OR x<0 OR we can say that: x IS (-inf , 0) U (5,+inf)

[2-]
Because its an linear equation, the domain is (R)

[3-]
because its fraction then the denominator should not be equal to 0 thats why we put : 2-t != 0 and we get t=2
Df = R - {2}

Try to resolve it by yourself
good luck