Question

if the domain is the set of integers, the solution set of x^2 -3x -4<0 is what?

Answer 1

What your question really asks for is,
"For what values of x does the corresponding parabola
y = x^2 - 3x - 4 fall below the x-axis?"

let's find the x-intercepts ....
x^2 - 3x - 4 = 0
(x-4)(x+1) = 0
x = -1 or x = 4

so the expression is < 0 for -1 < x < 4

or

(x+1)(x-4) < 0
( x+1 >0 AND x-4<0) OR ( x+1 < 0 AND x-4>0)
( x>-1 and x<4) OR (x<-1 AND x > 4)
x>-1 and x<4 OR (null set)

-1 < x < 4

Answer 2

thank you, so anything between -1 and 4 would be my answer? (0,1,2,3)?

Answer 3

yes.

Answer 4

Since your domain is integers, only the integers (0,1,2,3) satisfy the inequality. Otherwise, there would be an infinite number of non-integer solutions between -1 and 4.