Function, y = (2 times 3 x power + 1) divided by (4 times 3 x power - 3)

Function, y = (2 times 3 x power + 1) divided by (4 times 3 x power - 3)

Let a = 3 ^ X
Then a > 0
y=(2a+1)/(4a-3)
=(2a-3/2+5/2)/(4a-3)
=(2a-3/2)/(4a-3)+(5/2)/(4a-3)
=1/2+5/(8a-6)
a>0
So 8a-6 > - 6
1/(8a-6)0
5/(8a-6)0
1/2+5/(8a-6)1/2
Range (- ∞ - 1 / 3) ∪ (1 / 2, + ∞)