Solution:
Given:
[tex]w(x)=-(3x)^{\frac{1}{2}}-4[/tex]
Rewriting the function, by applying the law of fractional exponents,
[tex]a^{\frac{1}{2}}=\sqrt{a}[/tex]
Hence,
[tex]\begin{gathered} w(x)=-(3x)^{\frac{1}{2}}-4 \\ w(x)=-\sqrt{3x}-4 \end{gathered}[/tex]
The domain of a function is the set of all input values that make the function defined.
The function is undefined when the value of x under the root sign is less than zero because the square root of a negative number is complex.
Hence, the domain exists when x has a value greater than or equal to 0.
Therefore, the domain is;
[tex]Domain:x\ge0[/tex]
The range of a function is the set of all output values that makes the function defined.
Hence, the range exists when y is lesser than or equal to minus 4 because a value of y greater than -4, makes the function and domain undefined.
Therefore, the range is;
[tex]Range:w(x)\leq-4[/tex]
