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Algebra

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.

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  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.

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