Question

What is the RANGE of the function y = √x+5

A) Y ≥ -5
b) Y ≥ 0
c) Y ≥ √5
D) Y≥ 5


Also need the range of the funtion y= ³√x+8 but maybe it's one question per ask. Sorry if so...

Answer 1

Option D is correct Y≥ 5.

1)
`y= √(x)+5`-
`R=[5,\infty),[y|y\geq 5]`

2)
`y=\sqrt[3]{x}+8`-
`R=[-\infty,\infty),[y|y\geq \mathbb{R}]`

Explanation:

Given : Function
`y= √(x)+5`

To find : The range of the function

Solution : The function
`y=f(x)= √(x)+5`

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

`D=[0,\infty),[x|x\geq 0]`

As x takes values from 0 to
`\infty`,

then,
`√(x)+5` takes values from
`√(0)+5` =5 to
`√(\infty)+5=\infty`

Therefore, the range of the
`y= √(x)+5` is given by

`R=[5,\infty),[y|y\geq 5]`

Therefore, Option D is correct Y≥ 5.

Similarly, we can also find the range of
`y=\sqrt[3]{x}+8`

Firstly the domain of the function

`D=[-\infty,\infty),[x|x\geq \mathbb{R}]`

So, the range of the function is

`R=[-\infty,\infty),[y|y\geq \mathbb{R}]`