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

Try to determine whether the following function is even or odd: $f\left(x\right)=\frac{x}{x+1}$
I pass −x as input to the function to get: $f\left(-x\right)=\frac{-x}{-x+1}$
What is next step?
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Emilia Boyle
By definition, if $f\left(-x\right)=f\left(x\right)$ then f is even, and if $f\left(-x\right)=-f\left(x\right)$ then f is odd.
From your calculation, you found: $f\left(-x\right)=\frac{-x}{-x+1}$. This can be rewritten as follows
$\begin{array}{rl}f\left(-x\right)& =\frac{-x}{-x+1}\\ & =\frac{-\left(-x\right)}{-\left(-x+1\right)}\\ & =\frac{x}{x-1},\end{array}$
where in the second equality I multiplied both the numerator and the denominator of the fraction by $-1$. So, $f\left(x\right)$ is neither even nor odd.