SOLUTION: How do you determine whether {{{ f(x) = (X^2+1)/(x)}}} is an even, odd, or neither and what is its symmetry? If I recall correctly even tests are f(-x) = f(x), odd tests are f(-

Question 1121642: How do you determine whether is an even, odd, or neither and what is its symmetry?
If I recall correctly even tests are f(-x) = f(x), odd tests are f(-x) = -f(x) and even has a symmetry in respects to the y-axis and odd to the origin? But I don't know how to approach the above function.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

even tests are,
given:

=>
so, => is an even function

odd tests are
since above is proven that f(-x) = -f(x), means f(x) = (x^2 + 1)/x is an function

Since the function is , it is symmetric about the .

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

=

Both x and 1/x are odd functions; the sum of two or more odd functions is an odd function.

Therefore, is an odd function.
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