+170 Is the function \(f(x) = 5^x - 5^{-x}\) even, odd, or neither?
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.
