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Question 5 (2 marks)
Determine if the function [tex]$f(x)=\frac{4x}{x^2-1}$[/tex] is an odd or even function.
To determine whether the function [tex]\( f(x) = \frac{4x}{x^2 - 1} \)[/tex] is even, odd, or neither, we need to evaluate [tex]\( f(-x) \)[/tex] and compare it to [tex]\( f(x) \)[/tex] and [tex]\(-f(x)\)[/tex].
1. Calculate [tex]\( f(-x) \)[/tex]:
We start by substituting [tex]\(-x\)[/tex] into the function: [tex]\[
f(-x) = \frac{4(-x)}{(-x)^2 - 1}
\][/tex]
2. Simplify [tex]\( f(-x) \)[/tex]:
Simplify the expression for [tex]\( f(-x) \)[/tex]: [tex]\[
f(-x) = \frac{4(-x)}{x^2 - 1} = \frac{-4x}{x^2 - 1}
\][/tex]
3. Compare [tex]\( f(x) \)[/tex] and [tex]\( f(-x) \)[/tex]:
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