Question

what are the domain and range of f(x) = 2(3^x)? domain: (-∞,∞); range: (0,∞) domain: (-∞,∞); range: (2, ∞) domain: (0,∞); range-∞,∞) domain: (2,∞); range: (-∞,∞)

Answer 1

`f(x)2\cdot3^x\\\\the\ domain:\ x\in(-\infty;\ \infty)=\mathbb{R}\\\\the\ range:\ y\ib(0;\ \infty)`

Answer 2

A) domain: (-∞,∞); range: (0,∞)

Explanation:

The given function f(x) =
`2(3^x)`

Here x represents the domain and f(x) represents the range.

The given function is an exponential function.

The general form of an exponential function y =
`a.b^x`.

In the given equation, a =3 which is greater than 1. Therefore, when x increases the function f(x) tends to infinity.

When x decreases the function f(x) tends to zero.

That is, when x --> ∞, the function f(x) --> ∞

When x --> -∞, the function f(x) --> 0

Therefore, the function has the following domain and range.

Domain = (-∞, ∞)

Range = (0, ∞)