To find the domain and range of the function $F(x) = 3 + x$, let's examine each part in detail.

Domain:

The domain is the set of all possible input values for $x$ that make $F(x)$ valid. Here, $F(x) = 3 + x$ is a simple linear function with no restrictions on $x$, so:

$\text{Domain: } x \in (-\infty, \infty)$

Range:

The range is the set of all possible output values of $F(x)$. Since $F(x)$ is linear and can take any real number input, the output can also take any real number value.

$\text{Range: } F(x) \in (-\infty, \infty)$

Summary:

• Domain: $(-\infty, \infty)$
• Range: $(-\infty, \infty)$

Would you like more explanation, or have any questions on this?

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Relative Questions:

1. What is the domain and range of $G(x) = 2x + 5$?
2. How would the range change for a quadratic function like $H(x) = x^2 + 3$?
3. What is the domain of a function involving a square root, like $J(x) = \sqrt{x - 2}$?
4. For $K(x) = \frac{1}{x + 1}$, what values are excluded from the domain?
5. How does adding a constant affect the domain and range of a function?

Tip:

For any linear function $f(x) = mx + b$, both the domain and range are always $(-\infty, \infty)$, as there are no restrictions on $x$ or $f(x)$.