which statement best describes the domain and range of $f(x)=-(7)^x$ and $g(x)=7^x$?\n$f(x)$ and $g(x)$ have…

which statement best describes the domain and range of $f(x)=-(7)^x$ and $g(x)=7^x$?\n$f(x)$ and $g(x)$ have the same domain and the same range.\n$f(x)$ and $g(x)$ have the same domain but different ranges.\n$f(x)$ and $g(x)$ have different domains but the same range.\n$f(x)$ and $g(x)$ have different domains and different ranges.

which statement best describes the domain and range of $f(x)=-(7)^x$ and $g(x)=7^x$?\n$f(x)$ and $g(x)$ have the same domain and the same range.\n$f(x)$ and $g(x)$ have the same domain but different ranges.\n$f(x)$ and $g(x)$ have different domains but the same range.\n$f(x)$ and $g(x)$ have different domains and different ranges.

Answer

Explanation:

Step1: Determine domain of exponential functions

For any real - valued exponential function of the form (y = a^x) ((a>0,a\neq1)), the domain is all real numbers. For (f(x)=-(7)^x) and (g(x) = 7^x), the domain of both functions is ((-\infty,\infty)) since we can substitute any real number (x) into the functions.

Step2: Determine range of (g(x)=7^x)

Since (7>1), as (x\rightarrow-\infty), (7^x\rightarrow0) (but never reaches 0), and as (x\rightarrow\infty), (7^x\rightarrow\infty). So the range of (g(x)=7^x) is ((0,\infty)).

Step3: Determine range of (f(x)=-(7)^x)

For (f(x)=-(7)^x), as (x\rightarrow-\infty), (-(7)^x\rightarrow0) (but never reaches 0), and as (x\rightarrow\infty), (-(7)^x\rightarrow-\infty). So the range of (f(x)) is ((-\infty,0)).

Answer:

f(x) and g(x) have the same domain but different ranges.