Question

What are the domain and range of f(x) = 2(3X)?

Answer 1

Answer: Choice A

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

Range: $(0,\infty)$

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Explanation:

I'm assuming the function is $f(x) = 2(3)^x$ which is an exponential function.

The domain of any exponential function is the set of real numbers. In interval notation, the domain is $(-\infty, \infty)$ which says we can pick any number between negative infinity and positive infinity: aka any number we want. There are no restrictions to worry about such as division by zero errors.

The range of this exponential function is the set of y values such that y > 0. It often helps to see the graph of what is going on (see below). Note how as x heads to the left, and gets more negative, the curve approaches the x axis. It never actually touches it however. So it will never reach y = 0 itself but instead just get very close. The inequality y > 0 translates to the interval notation $(0,\infty)$

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Summary:

Domain: $(-\infty,\infty)$;  Range: $(0,\infty)$

So that's why the answer is choice A