Answer:
The range of the function is [0 , ∞) ⇒ answer B
Step-by-step explanation:
* lets revise the meaning of the domain and the range
- The domain is the values of x
- The domain is all the values of x which make the function is defined
- If there are some values of x make the function undefined, we
exclude these values from the domain
- The range is the values of f(x) which corresponding to the value of x
* Now lets look to the figure
∵ f(x) = √x
- We can not use the negative values for x because there is no
square root for negative numbers
∴ All real negative numbers make the function undefined
- We must exclude them from the domain
∴ The domain is all real numbers greater than or equal zero
∴ x ≥ 0
- To find the range use the first value of the domain
∵ the first value of x = 0
∴ f(0) = √0 = 0
∵ x can not be negative
∵ f(x) = √x
∴ f(x) can not be negative
∴ the range is all real numbers greater than or equal zero
∴ f(x) ≥ 0
OR
f(x) = [0 , ∞)
* The range of the function is [0 , ∞)
