Find the domain and range of $$ y=\log _{7}(4+3 x) $$. The domain is: The range is:

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To find the domain and range of the function $$ y = \log_{7}(4 + 3x) $$, we will analyze the expression inside the logarithm.

### Domain:
The logarithm is defined only for positive arguments. Therefore, we need to find when the expression $$ 4 + 3x $$ is greater than zero:

$$
4 + 3x > 0
$$

Subtracting 4 from both sides gives:

$$
3x > -4
$$

Dividing both sides by 3 yields:

$$
x > -\frac{4}{3}
$$

Thus, the domain of the function is:

$$
\text{Domain: } \left(-\frac{4}{3}, \infty\right)
$$

### Range:
The range of a logarithmic function is all real numbers. As $$ x $$ approaches $$-\frac{4}{3}$$ from the right, $$ 4 + 3x $$ approaches 0, and thus $$ y $$ approaches $$-\infty$$. As $$ x $$ increases without bound, $$ 4 + 3x $$ also increases without bound, and $$ y $$ approaches $$ +\infty $$.

Therefore, the range of the function is:

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

### Summary:
- The domain is $$ \left(-\frac{4}{3}, \infty\right) $$.
- The range is $$ (-\infty, \infty) $$.
The domain is $$ \left(-\frac{4}{3}, \infty\right) $$ and the range is $$ (-\infty, \infty) $$.

Find the domain and range of .
The domain is:
The range is:

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