SOLUTION: 1) Find the domain of the following: b) g(x)=5e^x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1) Find the domain of the following: b) g(x)=5e^x       Log On


   

Question 116012: 1) Find the domain of the following:
b) g(x)=5e^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
b)

If you have something like 1%2Fx, then you have to keep in mind that x%3C%3E0 since division by zero is undefined. If you have something like sqrt%28x%29, then you have to keep in mind that x%3E=0 since you cannot take the square root of a negative number. If you have something like log%28x%29 or ln%28x%29, then you have to keep in mind that x%3E0 since you cannot take the log of zero or a negative number. These are examples of restrictions of the domain.




Since the function g%28x%29=5e%5Ex 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%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+5%2Aexp%28x%29%29+ Graph of g%28x%29=5e%5Ex
----------------------------------
Answer:

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

Here's the domain in interval notation: