What is the domain and range of the function g of x equals 2x squared plus 3 divided by 5x squared minus 5?

Answer 1

g(x) = 2x2 + 3x - 5

g(x) is a parabolic function. To find it's range, let's find it's lowest point by getting the location at which it has a slope of 0.

g'(x) = 4x + 3
0 = 4x + 3
4x = -3
x = -3/4

Now find it's value at that point:

(-3/4)2 + 3(-3/4) - 5
= 9/16 - 9/4 - 5
= (9 - 36 - 80) / 16
= -107/16

So it's lowest value is -107/16
∴ {g(x) | g(x) ≥ -107/16, g(x) ∈ N}