Question

Determine whether each function is even, odd, or neither.

f(x) = Vx2-9
DONE
g(x) = |x-3|
DONE
f(x) = x\x^2-1
DONE
g(x) = x + x2
DONE

Answer 1

A function is even if f(x) = f(-x), odd if f(x) = -f(-x), and neither if neither condition is satisfied. Analyzing the given functions, the first and second functions are neither even nor odd, the third function is odd, and the fourth function is neither even nor odd.

Step-by-step explanation:

A function is considered even if f(x) = f(-x) for every value of x in the domain. On the other hand, a function is considered odd if f(x) = -f(-x) for every value of x in the domain. If neither of these conditions is satisfied, then the function is considered neither even nor odd.

Let's analyze each of the given functions:

1. f(x) = √x^2-9
   This function is neither even nor odd, as it does not satisfy the conditions for evenness or oddness.
2. g(x) = |x-3|
   This function is neither even nor odd, as it does not satisfy the conditions for evenness or oddness.
3. f(x) = x/(x^2-1)
   This function is odd, as it satisfies the condition f(x) = -f(-x) for every value of x in the domain.
4. g(x) = x+x^2
   This function is neither even nor odd, as it does not satisfy the conditions for evenness or oddness.

Therefore,

1) Function is neither even nor odd.

2) Function is neither even nor odd.

3) Function is odd.

4) Function is neither even nor odd.

"Your question is incomplete, probably the complete question/missing part is:"

Determine whether each function is even, odd, or neither.

f(x)= √x^2-9

g(x)=|x-3|

f(x)=x/(x^2-1)

g(x)=x+x^2