Question 116015
d)


If you have something like {{{1/x}}}, then you have to keep in mind that {{{x<>0}}} since division by zero is undefined. If you have something like {{{sqrt(x)}}}, then you have to keep in mind that {{{x>=0}}} since you cannot take the square root of a negative number. If you have something like {{{log(x)}}} or {{{ln(x)}}}, then you have to keep in mind that {{{x>0}}} since you cannot take the log of zero or a negative number. These are examples of restrictions of the domain.




Since the function {{{g(t)=5^t}}} does not have a division by x, a square root, or a logarithm function, this means we don't have to worry about domain restrictions. 


Also, notice if we graph the function, we can see that there are no domain restrictions:


{{{ graph( 500, 500, -10, 10, -10, 10, 5^x) }}}  Graph of {{{g(t)=5^t}}} 


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Answer:


So the domain is the set of all real numbers. In other words, t can be any real number.


Here's the domain in interval notation:

*[Tex \LARGE \left(-\infty,\infty\right)]