What are the domain and range of $$ f(x)=2\left(3^{x}\right) $$ ? domain: $$ (-\infty, \infty) $$; range: $$ (0, \infty) $$ domain: $$ (-\infty, \infty) $$; range: $$ (2, \infty) $$ domain: $$ (0, \infty) $$; range: $$ (-\infty, \infty) $$ domain: $$ (2, \infty) $$; range: $$ (-\infty, \infty) $$

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UpStudy AI · Accepted Answer

The function is given by

$$
f(x)=2\left(3^{x}\right)
$$

**Step 1: Find the Domain**

The domain of an exponential function $$ 3^x $$ is all real numbers $$\left(-\infty, \infty\right)$$. Multiplying by 2 does not affect the domain. Thus, the domain of $$ f(x) $$ is

$$
(-\infty, \infty)
$$

**Step 2: Find the Range**

The basic exponential function $$ 3^x $$ has a range of

$$
(0, \infty)
$$

since $$ 3^x > 0 $$ for all $$ x $$ in $$\mathbb{R}$$.

Multiplying by 2 scales the output, but the inequality remains unchanged (because 2 is positive). That is,

$$
f(x)=2\left(3^{x}\right) > 0
$$

Therefore, the range of $$ f(x) $$ remains

$$
(0, \infty)
$$

**Conclusion:**

The domain of $$ f(x) $$ is $$(-\infty, \infty)$$ and the range is $$(0, \infty)$$.

Thus, the correct answer is:

- domain: $$(-\infty, \infty)$$; range: $$(0, \infty)$$
The domain is all real numbers, and the range is all positive real numbers.

What are the domain and range of ?
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