composite function - implied range?

[tonychet2]

how do i find the implied range of F(g(X))

if f(x) = e^x
and g(x) = -x^2
THANKS!

[Hancock]

Now, let's look at the function. Any exponent that we have will never allow the exponential to be negative or be zero. This is a basic exponential / log law. So the lower bound of our range is 0, non-inclusive.


We can also note that our exponent will be negative for all values of x (excluding x = 0, where the exponent will be 0). This tells us that the function will always be below 1, inclusive, since x = 0 will cause e^(-0^2) = 1.

So our implied range is (0,1].