#1**+1 **

We can simplify $ f(x) = 5^x - 5^(-x) $ down to:

\[ f(x) = 5^x - 1/(5^x) \]

(This will be easier to deal with).

Also, we have to substitute in -x for x in f(x) to find out if the function is even, odd, or neither:

\[ f(-x) = 5^(-x) - 5^x \]

\[ f(-x) = 1/(5^x) - 5^x \]

\[ f(-x) = - (5^x - 1/(5^x) \]

When we compare the 2 functions we see that the new function differs by a multiple of -1 meaning that its odd:

\[ f(x) = 5^x - 1/(5^x) \]

\[ f(-x) = - (5^x - 1/(5^x) \]

In conclusion, the answer is $ f(x) = 5^x - 5^(-x) $ is ODD.

Guest Jun 29, 2019