find the domain of the function in interval notation? g(x)=5 over 2x^2+x-1

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I think your function is g(x)=5/(2x^2+x-1)The domain is just the list of x-values that "work" for the function...that is, they return some real number y-value. In your case, the denominator cannot be zero. I'm going to try to factor the denominator so I can more easily see what values of x would make that quadratic expression equal to zero.g(x)=5/[(2x-1)(x+1)]That worked out nicely. From that, I can see that if x = 1/2 or if x = -1, then the denominator would have a value of zero...that would make g(x) undefined...which is bad.EVERY other real number value of x "works". In this case, it's easier to list the values that don't work.The domain is x is not equal to either -1 or 1/2. This implies that x can be anything else.