Question

F(x)= cubed root of x-2 +3A. What is the domain of this function? Explain your answerB. What is the range

Answer 1

Given data:

`F(x)=\sqrt[3]{x-2}+3`

A. The domain of cube root function is all the real numbers because it is possible for three negatives to equal a negative. But this cannot apply for square functions.

B. For range put F(x) = y

`\begin{gathered} y=\sqrt[3]{x-2}+3 \\ y-3=\sqrt[3]{x-2} \end{gathered}`

Now, taking cube both sides we get

`(y-3)^3=x-2`
`x=2+(y-3^{})^3`

Thus, the range for the function is also all real numbers because value of x will be defined for every value of y.