what are the domain and range of f(x) = 2(3^x)?\no domain: (-∞,∞); range: (0,∞)\no domain: (-∞,∞); range…

what are the domain and range of f(x) = 2(3^x)?\no domain: (-∞,∞); range: (0,∞)\no domain: (-∞,∞); range: (2,∞)\no domain: (0,∞); range: (-∞,∞)\no domain: (2,∞); range: (-∞,∞)

what are the domain and range of f(x) = 2(3^x)?\no domain: (-∞,∞); range: (0,∞)\no domain: (-∞,∞); range: (2,∞)\no domain: (0,∞); range: (-∞,∞)\no domain: (2,∞); range: (-∞,∞)

Answer

Answer:

A. domain: $(-\infty,\infty)$; range: $(0,\infty)$

Explanation:

Step1: Determine the domain

For an exponential - type function $y = a\cdot b^{x}$ (in this case $f(x)=2\cdot3^{x}$), $x$ can take any real - number value. So the domain is all real numbers, which is written as $(-\infty,\infty)$.

Step2: Analyze the range

Since $3^{x}>0$ for all real values of $x$ (the exponential function $y = b^{x}$ with $b>1$ is always positive), and $f(x)=2\cdot3^{x}$, then $f(x)>0$. So the range of the function $f(x)$ is $(0,\infty)$.