Question

Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = x + 4/x

Answer 1

Answer:

The given function is an odd function.

Step-by-step explanation:

We define a function f(x) as even function when f(-x) = f(x) and odd function when f(-x) = - f(x) and otherwise it is neither even nor odd function.

Now, we are given a function of x as $f(x) = x + \frac{4}{x}$ and we have to deternime whether the function f(x) is even, odd, or neither even nor odd.

Now, $f(-x) = - x + \frac{4}{- x} = - x - \frac{4}{x} = - [x + \frac{4}{x}] = - f(x)$

Therefore, the given function is an odd function. (Answer)