Find the domain of the function. g(x) = √x /(8x^2 + 7x − 1)

Answer 1

The numerator cannot handle a negative value for x, so negative values are outside of the domain. The denominator factors into (x+1)(8x-1) and it cannot be zero since the function, g, calls for dividing by it. So we have to remove -1, but no problem, we already removed it in the numerator step. We also have to remove 1/8 which would make the second factor, 8x-1, zero.

So after we take out all the values that would make g impossible to evaluate, we are left with all non-negative real numbers except 1/8 as the domain, which can be written written as {x s.t. x ≥ 0 and x ≠ 1/8 } or [0,1/8) ∪ (1/8, ∞).