Answer:
Option D is correct Y≥ 5.
1)[tex]y= \sqrt{x}+5[/tex]- [tex]R=[5,\infty),[y|y\geq 5][/tex]
2) [tex]y=\sqrt[3]{x}+8[/tex]- [tex]R=[-\infty,\infty),[y|y\geq \mathbb{R}][/tex]
Step-by-step explanation:
Given : Function [tex]y= \sqrt{x}+5[/tex]
To find : The range of the function
Solution : The function [tex]y=f(x)= \sqrt{x}+5[/tex]
The range of a function y=f(x) is the set of values y takes for all values of x within the domain of y=f(x).
The domain of given function f(x) is the set of all values of x in the interval
[tex]D=[0,\infty),[x|x\geq 0][/tex]
As x takes values from 0 to [tex]\infty[/tex],
then, [tex] \sqrt{x}+5[/tex] takes values from [tex] \sqrt{0}+5[/tex] =5 to [tex] \sqrt{\infty}+5=\infty[/tex]
Therefore, the range of the [tex]y= \sqrt{x}+5[/tex] is given by
[tex]R=[5,\infty),[y|y\geq 5][/tex]
Therefore, Option D is correct Y≥ 5.
Similarly, we can also find the range of [tex]y=\sqrt[3]{x}+8[/tex]
Firstly the domain of the function
[tex]D=[-\infty,\infty),[x|x\geq \mathbb{R}][/tex]
So, the range of the function is
[tex]R=[-\infty,\infty),[y|y\geq \mathbb{R}][/tex]
