Answer:
[tex]y = - \sqrt{x - 5} + 3[/tex]
Step-by-step explanation:
The function [tex]y = - \sqrt{x - 5} + 3[/tex] has a domain x ≥ 5.
This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.
Hence, (x - 5) ≥ 0
⇒ x ≥ 5
Now, for all x values that are greater than equal to 5 the value of [tex]- \sqrt{x - 5}[/tex] will be negative.
So, [tex]- \sqrt{x - 5} \leq 0[/tex]
⇒ [tex]- \sqrt{x - 5} + 3 \leq 3[/tex]
⇒ y ≤ 3
Therefore, the range of the function is y ≤ 3. (Answer)
