Question

What is the range of the function f(x)=e^x/e^x+c? Assume that c is a constant greater than zero.

Answer 1

`f(x)=(e^x)/(e^x+c)`

For all
`x`, we know that
`e^x>0`. We're assuming that
`c>0`, so for sure we know that
`f(x)>0`. We also know that
`e^x+c>e^x`, so
`f(x)<1`.



`f` is continuous, since
`e^x+c\\eq0` for any
`x`. So the range is
`0<f(x)<1`.

Answer 2

The range is all of the numbers from 0 to 1.

0< x > 1

Explanation:

In order to solve this you have to remember that the Range of a function is the values that the dependant of the function is able to take, since this is a division of a number between itself plus a constant greater than zero, the division will never be equal to 1, and it would never be smaller than zero, because it is dividing by itself, so the answer would be all of the numbers that are greater than zero but smaller than one.