What is the domain of
4w2 – 9/
–5w
The domain of rational functions is all reals except where the denominator is zero.
If your denominator is 5w, then only w=0 is excluded.
To find the domain of the expression 4w^2 - 9 / -5w, we need to consider two things:
1. The expression 4w^2 - 9 must not have any restrictions on the value of w. Since it is a quadratic expression, there are no restrictions, and it is defined for all real values of w.
2. The expression -5w in the denominator must not be equal to zero, as division by zero is undefined. Therefore, we need to find the values of w for which -5w = 0. Solving this equation, we get w = 0.
In summary, the domain of the expression 4w^2 - 9 / -5w is all real numbers except 0.
To find the domain of a rational function like (4w^2 - 9)/(-5w), we need to determine the values of w that would result in division by zero. Since division by zero is undefined, those values cannot be included in the domain.
To find the values that make the denominator zero, we need to set the denominator to zero and solve for w:
-5w = 0
Dividing both sides by -5, we get:
w = 0
Therefore, w = 0 would make the denominator zero, which is not allowed. Hence, the domain of the function would be all real numbers except 0.
In interval notation, the domain would be (-∞, 0) U (0, +∞).