Find the Domain 5z+2w^2=8

Problem

5*z+2*w2=8

Solution

1. Identify the variables in the equation. The equation 5*z+2*w2=8 defines a relationship between two variables, z and w

2. Solve for the dependent variable z in terms of the independent variable w

5*z=8−2*w2

z=(8−2*w2)/5

3. Analyze the resulting function z=ƒ(w) The expression (8−2*w2)/5 is a polynomial divided by a non-zero constant.

4. Determine any restrictions. Since there are no square roots of negative numbers, no logarithms, and no variables in the denominator, there are no values of w that make the expression undefined.

5. Conclude that the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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