If f(x) = 2x + 1, what is the domain?

Question 4 Select one:

a.

(2, 1]

b.

(1, 2)

c.

[–∞,∞]

d.

(–∞,∞)

e.

(∞,–∞)

The function \( f(x) = 2x + 1 \) is a linear function. Linear functions are defined for all real values of \( x \) since there are no restrictions like square roots or divisions by zero. Therefore, the domain of this function is all real numbers.

In interval notation, this is expressed as:

**Domain:** \( (-\infty, \infty) \)

So, the correct answer is:

**d. \( (-\infty, \infty) \)**

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Would you like more details or have any questions?

Here are 5 related questions for further understanding:
1. What is the range of the function \( f(x) = 2x + 1 \)?
2. How would the domain change if the function were \( f(x) = \frac{1}{2x + 1} \)?
3. What is the slope of the function \( f(x) = 2x + 1 \)?
4. How do you graph the function \( f(x) = 2x + 1 \)?
5. What is the inverse of the function \( f(x) = 2x + 1 \)?

**Tip:** When determining the domain of a function, look for any operations that may restrict the values of \( x \), such as square roots, denominators, or logarithms.

If f(x) = 2x + 1, what is the domain?

Question 4 Select one:

a. (2, 1]

b. (1, 2)

c. [–∞,∞]

d. (–∞,∞)

e. (∞,–∞)

Understand how to determine the domain of the linear function f(x) = 2x + 1. This problem explains key algebraic concepts and covers the domain of linear functions. Suitable for students in Grades 9-10.

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