Solution: x ≥ -5
Domain Definition: The domain of a function is the set of input or argument values for which the function is real and defined
squareroot 2x + 10 ⇒ 2x + 10 ≥ 0
Solve 2x + 10 ≥ 0:
Subtract 10 from both sides
2x + 10 - 10 ≥ 0 - 10
Simplify
2x ≥ -10
Divide both sides by 2
2x / 2 ≥ -10 / 2
Simplify
2x / 2
Divide the numbers: 2 / 2 = 1
= x
Note: x has the same value as 1
Divide the numbers: -10 / 2 = -5
= -5
The function domain is
x ≥ -5
Answer:
[tex]\boxed{\text{C. }x \geq -5}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x-values that will make the function work.
The definition automatically eliminate options B and D.
Your function is
[tex]y = \sqrt{2x + 10}[/tex]
The number under the radical cannot be negative, because the square root of a negative number is imaginary.
Thus, we must have
[tex]\begin{array}{rcr}2x+ 10 & \geq & 0\\2x & \geq & -10\\x & \geq & -5\\\end{array}\\\\\text{The domain is }\boxed{\mathbf{x \geq -5}}[/tex]
The graph of your function shows that the range is x ≥ -5.
