Let f(x) be the function f(x) = 5^x - 5^{-x}. Is f(x) even, odd, or neither ? Prove your result.

1 Answer
Feb 6, 2018

The function is odd.

Explanation:

If a function is even, it satisfies the condition:

f(-x)=f(x)

If a function is odd, it satisfies the condition:

f(-x)=-f(x)

In our case, we see that

f(-x)=5^-x-5^x=-(5^x-5^-x)=-f(x)

Since f(-x)=-f(x), the function is odd.