The reason why the domain of g(x)=5⁻ˣ has a domain of all real numbers while the range is not is because, every real number value of x makes perfect sense as an exponent, that means there no restrictions because there are divisions by zero or the square root of the negative number.
The reason why the range is not all real number is because of the negative exponent. This will limit the range to positive real numbers only.
