![f(x)=\sqrt[]{3x+1}](https://img.qammunity.org/2023/formulas/mathematics/high-school/5w27qu4ol0lvqprtb6euulmlg47reu0cu7.png)
The domain of a functio f(x) is the set of vlues for which the function is defined (all the values of x for which the function is defined).
Range: the values that f(x) takes.

Find the values of x when f(x) is greather than or equal to 4 and less than or equal to 5
When f(x)≥4
![\begin{gathered} 4\leq\sqrt[]{3x+1} \\ 4^2\leq(\sqrt[]{3x+1})^2 \\ 16\leq3x+1 \\ 16-1\leq3x \\ 15\leq3x \\ (15)/(3)\leq x \\ \\ 5\leq x \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/vu0k4zklecc0se17wr5ig6gfbrhsvqol3z.png)
When f(x)≤5
![\begin{gathered} 5\ge\sqrt[]{3x+1} \\ 5^2\ge(\sqrt[]{3x+1})^2 \\ 25\ge3x+1 \\ 25-1\ge3x \\ 24\ge3x \\ (24)/(3)\ge x \\ \\ 8\ge x \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/7z488eggd884us04ijadz0nbixxjprmki7.png)
Then. the domain in that interval of range is:
