Answer:
f(x) and g(x) have the same domain but different ranges.
Step-by-step explanation:
The domain of [tex]f(x)=-(7)^x[/tex] is:
[tex]Domain: (-\infty, \infty)[/tex]
Because there is no any restriction. And its range is:
[tex]Range: \{y\in R :y<0\}[/tex]
Because the minus sign is out of the parentheses, so no matter the value of x, the result will be always negative.
Now, The domain of [tex]f(x)=7^x[/tex] is:
[tex]Domain: (-\infty, \infty)[/tex]
As before, because there is no any restriction. And its range is:
[tex]Range: \{y\in R :y>0\}[/tex]
Because no matter the value of x this function is always positive since:
[tex]a^{-x}=\frac{1}{a^x}[/tex]
Therefore:
f(x) and g(x) have the same domain but different ranges.
I attached you the graphs.
