Questions: Find the domain of the function. f(x)=5x+7 Determine the domain of f(x). Choose the correct answer below. A. (-∞, 5) B. (-∞, 7) or (7, ∞) C. (5, ∞) D. (-∞, ∞)

Find the domain of the function. f(x)=5x+7 Determine the domain of f(x). Choose the correct answer below. A. (-∞, 5) B. (-∞, 7) or (7, ∞) C. (5, ∞) D. (-∞, ∞)
Transcript text: Find the domain of the function. \[ f(x)=5 x+7 \] Determine the domain of $f(x)$. Choose the correct answer below. A. $(-\infty, 5)$ B. $(-\infty, 7)$ or $(7, \infty)$ C. $(5, \infty)$ D. $(-\infty, \infty)$
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Solution

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Solution Steps

Step 1: Identify the type of function

The given function is \( f(x) = 5x + 7 \), which is a linear function.

Step 2: Determine the domain of a linear function

For linear functions, the domain is all real numbers because there are no restrictions on the input \( x \).

Step 3: Match the domain with the given options

The domain of \( f(x) = 5x + 7 \) is \( (-\infty, \infty) \), which corresponds to option D.

Final Answer

The correct answer is D. \( \boxed{(-\infty, \infty)} \)

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