2 Answers

Warlord · Answer 1 · 2020-10-17T15:20:34+0000

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

Satish Singh · Answer 2 · 2020-10-19T16:27:42+0000

Answer:

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

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 = √(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.