Question

Find the range of the functiong(x) = 5 + / 4 - x​

Answer 1

Answer:

The range of g(x) is [5, ∞) ⇒ (a)

Step-by-step explanation:

The range of the function is the values of y which corresponding to the values of x (domain)

∵ $g(x)=5+\sqrt{4-x}$

∵ There is no square root for negative values

∴ 4 - x ≥ 0

→ Add x to both sides

∴ 4 - x + x ≥ 0 + x

∴ 4 ≥ x

→ that means x is smaller than or equal to 4

∴ x ≤ 4

→ The greatest value of x = 4

∴ The domain of g(x) = {x : x ≤ 4} ⇒ (-∞, 4]

→ At x = 4

∵ g(4) = 5 + $\sqrt{4-4}$

∴ g(4) = 5 + 0

∴ g(4) = 5

→ That means the smallest value of y = 5 because  $\sqrt{4-x}$ is always

   give a positive value which add to 5

∴ The range of g(x) is {y : y ≥ 5} ⇒ [5, ∞)

The right answer is (a)