Question

what is the domain of the function Y= square root 2x+10 explain and show work ) A. X≥5 B. Y≥5 C. X≥-5 D. Y≤-5 ​

Answer 1

Solution: x ≥ -5

Steps

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 2

Answer:

$\boxed{\text{C. }x \geq -5}}$

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

$y = \sqrt{2x + 10}$

The number under the radical cannot be negative, because the square root of a negative number is imaginary.

Thus, we must have

$\begin{array}{rcr}2x+ 10 & \geq & 0\\2x & \geq & -10\\x & \geq & -5\\\end{array}\\\\\text{The domain is }\boxed{\mathbf{x \geq -5}}$

The graph of your function shows that the range is x ≥ -5.