Determine whether the function is even, odd, or neither.
f(x)= 7x^(3/4)
How do you do this with a fraction?
To determine if a function is even, odd, or neither, we need to analyze the function's behavior with respect to both positive and negative values of x.
A function f(x) is even if f(x) = f(-x) for all x in the domain. This means that substituting -x into the function should give the same result as substituting x.
On the other hand, a function f(x) is odd if f(x) = -f(-x) for all x in the domain. This means that substituting -x into the function should give the negative of the result obtained by substituting x.
Let's apply this to the given function f(x) = 7x^(3/4):
1. Even property: We substitute -x into the function and simplify:
f(-x) = 7(-x)^(3/4)
= 7*(-1)^(3/4)*x^(3/4)
= 7*(-1)*x^(3/4)
= -7x^(3/4)
Since f(-x) = -7x^(3/4) ≠ f(x), the function does not satisfy the even property.
2. Odd property: We substitute -x into the function and simplify:
-f(-x) = -(-7x^(3/4))
= 7x^(3/4)
Since f(-x) = 7x^(3/4) ≠ -f(x), the function does not satisfy the odd property either.
Therefore, we can conclude that the function f(x) = 7x^(3/4) is neither even nor odd.