Question

What is the domain of the function y= √ x+4?

a) x<−4
b) x≤−4
c) x≥−4
d) x>−4

Answer 1

The domain of the function y = √(x+4) is the set of all x-values for which the inside of the square root is non-negative. Solving the inequality x + 4 ≥ 0 gives x ≥ -4, so the correct domain is c) x ≥ -4.

Step-by-step explanation:

The domain of the function y = √(x+4) refers to the set of all possible x-values for which the function is defined. Since the square root function is defined only for non-negative numbers, the expression inside the square root, x + 4, must be greater than or equal to zero. Hence, we need to solve the inequality x + 4 ≥ 0.

To find the domain, we subtract 4 from both sides of the inequality:

• 
  
• x + 4 ≥ 0

• x ≥ -4
• 
  

Therefore, the correct answer is c) x ≥ -4.