Find the domain of the function using interval √x/(4x²+3x-1)

Question

I solved 4x²+3x-1=0
I got (1/4,-1) but idk what to do

Answer 1

suppose we have y = √x/(4x²+3x-1)
There are two restrictions we have to worry about
1. The denominator can't be zero. You appear to have taken care of that
and found the values of x which make it zero
So we have to put on the restriction that x ≠ -1 and x ≠ 1/4
2. √x would be undefined if x is negative, so x ≥ 0

your domain would be all real values of x, x≥ 0 , x ≠ 1/4

(notice the x ≠ -1 is already taken care of with x ≥ 0)

Answer 2

Thanks