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

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Answer 1 · 2018-02-06T15:35:35

The function is odd.

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.