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

aphathalo

aphathalo

Answered question

2022-10-03

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
What is next step?

Answer & Explanation

Emilia Boyle

Emilia Boyle

Beginner2022-10-04Added 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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