Try to determine whether the following function is even or odd: f(x)=(x)/(x+1)

aphathalo 2022-10-03 Answered
Try to determine whether the following function is even or odd: f ( x ) = x x + 1
I pass −x as input to the function to get: f ( x ) = x x + 1
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Answers (1)

Emilia Boyle
Answered 2022-10-04 Author has 10 answers
By definition, if f ( x ) = f ( x ) then f is even, and if f ( x ) = f ( x ) then f is odd.
From your calculation, you found: f ( x ) = x x + 1 . This can be rewritten as follows
f ( x ) = x x + 1 = ( x ) ( x + 1 ) = x x 1 ,
where in the second equality I multiplied both the numerator and the denominator of the fraction by 1. So, f ( x ) is neither even nor odd.
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