Question

Help me on this please

Answer 1

Answer:

domain x ≥ 7

range y ≥ 9

The 3rd answer

Step-by-step explanation:

* Lats talk about the domain and the range of the function

- The domain is the all values of x which make the function is defined

- The range is all the values of y got from the defined values of x

- In the square roots or any even roots the value under it must be

 greater than or equal to zero ( the even roots for negative values is

 undefined)

* Lets solve our problem

∵ $f(x)=\sqrt{x-7}+9$

- In this function we must chose the values of x which makes

 x - 7 zero or positive value

∴ Let x - 7 ≥ 0

- Now solve the inequality

∵ x - 7 ≥ 0 ⇒ add 7 to the both sides

∴ x ≥ 7

- The domain of the function is the values of x

∴ The domain of the function is x ≥ 7

- Lets use the first value of x to find the first value of y

∵ x = 7

∴ f(7) = √(7 - 7) + 9 = √0 + 9 = 9

- The first value of the range is 9

∵ The range is values of y corresponding to the values of x

∴ The range of the function is y ≥ 9

* The domain x ≥ 7

 The range y ≥ 9

Answer 2

Domain: x is greater than or equal to 7

Range: y is greater than or equal to 9