Question

Find the domain of the function. (Write your answer using interval notation.)


sqrt(x)/
(4x^2 + 3x − 1)

If you set the bottom equal to zero, I got that x can't be -1 or 1/4. But I'm not sure if that's right, or how to write the answer in interval notation.

Answer 1

Y = 4x^2 + 3x - 1. Factor it:

A*C = 4*(-1) = -4.
4x^2 + (4x-x) - 1.
4x^2+4x - (x+1).
4x(x+1) - (x+1).
Y = (x+1)(4x-1).

All real values of x will give a real
output. Therefore, the domain is all real values of x.

Interval notation:
-infinity < X < +infinity.

So x must be greater than (-)infinity but less than +infinity.