Given data:
[tex]F(x)=\sqrt[3]{x-2}+3[/tex]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
[tex]\begin{gathered} y=\sqrt[3]{x-2}+3 \\ y-3=\sqrt[3]{x-2} \end{gathered}[/tex]Now, taking cube both sides we get
[tex](y-3)^3=x-2[/tex][tex]x=2+(y-3^{})^3[/tex]Thus, the range for the function is also all real numbers because value of x will be defined for every value of y.