Question

the function f(x) = x 1\2 is transformed to get function w.w(x) = -(3x)^1\2 -4what are the domain and the range of the function w?domain: x > ____?range: w(x)<____?

Answer 1

To make things easier, convert the form of the function, from algebraic to root

$\begin{gathered} w(x)=-(3x)^{\frac{1}{2}}-4 \\ w(x)=-\sqrt[]{3x}-4 \end{gathered}$

For this function, the domain can't include negative values due to the square root. It means

$D\colon\text{ x}\ge0$

To define the range, evaluate the function in the lower value of the domain (which is 0)

$\begin{gathered} w(0)=-\sqrt[]{3\cdot0}-4 \\ w(0)=-4 \end{gathered}$

The range include all values that are less than or equal to -4

$R\colon w(x)\leq-4$