Determine algebraically whether the function is even, odd, or neither even nor odd. f(x)=x+ (4)/(x) a))Even b))Neither c))Odd

Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x)=x+
`(4)/(x)`

a))Even
b))Neither
c))Odd

Answer 1

the function is odd just substitute f(x) for f(-x) and replace all the x's with -x's then go back to the original problem and substitute f(x) for -f(x) and multiply the original problem by -1 and since f(-x) and -f(x) are equal, it is odd. if the original problem, f(x) and f(-x) were equal it would be even and if none of the three are equal it would be neither. the answer to this question is odd because f(-x) and -f(x) are equal.