Question 21787: Look at the function:G(x)= e^x
What is the domain and range of this funciton?
Look at the funticon: H(x)= ln(x)
What is the domain and range of this function?
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! Look at the function:G(x)= ex
What is the domain and range of this function?
`
The domain is the set of all possible values of x which can be substituted for x. Since any positive number (and "e" is a positive number 2.718...) can be raised to the power of any real number, the domain is "all real numbers", or in interval notation (-oo, oo).
`
The range is the set of values obtained by substituting values of the domain into the function's equation. Any real power of any positive number is always positive, whether the exponent is positive, negative or 0. So the range is "all positive numbers", or in interval notation (0, oo)
`
`
Look at the funtion: H(x)= ln(x)
What is the domain and range of this function?
`
This is the inverse function of G(x)=ex. Thus it's domain is the range of its inverse function and its range is the domain of its inverse function. So:
`
Domain: (0, oo), Range = (-oo, oo)
`
Edwin
AnlytcPhil@aol.com
|
|
|
