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

 Jun 29, 2019
 #1
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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.

 Jun 29, 2019
 #2
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I am SuerBoranJacobs and have forgotten my password. Now I have to be a guest...

sad

Guest Jun 29, 2019
 #3
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Is the function  even, odd, or neither?

laugh

 Jun 29, 2019
edited by Omi67  Jun 29, 2019

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