Question

the function f(x) = x^1/2 is transformed to get function W.w(x)= -(3x)^1/2 - 4 what are the domain and the range of function w? domain : x is grater then or equal to ___range : w(x) is less than or equal to ___(picture listed below)

Answer 1

Given:

`w(x)=-(3x)^{(1)/(2)}-4`

Rewriting the function, by applying the law of fractional exponents,

`a^{(1)/(2)}=√(a)`

Hence,

`\begin{gathered} w(x)=-(3x)^{(1)/(2)}-4 \\ w(x)=-√(3x)-4 \end{gathered}`

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;

`Domain:x\ge0`

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;

`Range:w(x)\leq-4`