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lana [24]
3 years ago
8

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 ​

Mathematics
2 answers:
Anna [14]3 years ago
6 0

Solution: x ≥ -5

<h2>Steps</h2>

Domain Definition: The domain of a function is the set of input or argument values for which the function is real and defined

<u>squareroot 2x + 10</u>  ⇒  <u>2x + 10 ≥ 0</u>

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: <u>2 / 2 = 1</u>

= x

Note: x has the same value as 1

Divide the numbers: -10 / 2 = -5

= -5

The function domain is

x ≥ -5

Art [367]3 years ago
3 0

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.

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