Question

find the domain of the function.

(f(x) = 2x + 7)

a. (\\{x \mid x > 0\\})
b. all real numbers
c. (\\{x \mid x \
eq 0\\})
d. (\\{x \mid x \geq -7\\})

Explanation:

Identify the function type

Using the Linear Function Domain knowledge point

$$ f(x) = 2x + 7 $$

Determine the domain restrictions

Using the Domain and Range knowledge point

$$ \text{No division by zero, square roots of negative numbers, or logarithms exist.} $$

State the final domain

Using the Linear Function Domain knowledge point

$$ \text{Domain} = (-\infty, \infty) \quad \text{or} \quad \text{all real numbers} $$

Answer:

• A. \(\{x | x > 0\}\)
• B. all real numbers (Correct answer)
• C. \(\{x | x

eq 0\}\)

• D. \(\{x | x \geq -7\}\)