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

Question

1419 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-06T15:35:35

The function is odd.

If a function is even, it satisfies the condition:

$f (- x) = f (x)$ $f(-x)=f(x)$

If a function is odd, it satisfies the condition:

$f (- x) = - f (x)$ $f(-x)=-f(x)$

In our case, we see that

$f (- x) = 5^{- x} - 5^{x} = - (5^{x} - 5^{- x}) = - f (x)$ $f(-x)=5^-x-5^x=-(5^x-5^-x)=-f(x)$

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

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