# How do you determine if #f(x)= 1 - X^(1/3)# is an even or odd function?

odd function

because

thus it's a strange function.

By signing up, you agree to our Terms of Service and Privacy Policy

To determine if a function ( f(x) = 1 - x^{1/3} ) is even or odd, we can examine its symmetry properties:

- Even functions satisfy the condition: ( f(-x) = f(x) ).
- Odd functions satisfy the condition: ( f(-x) = -f(x) ).

Substituting ( -x ) into the function and simplifying, we have:

[ f(-x) = 1 - (-x)^{1/3} = 1 + x^{1/3} ]

Comparing ( f(-x) ) with ( f(x) ), we observe that ( f(-x) ) is not equal to ( f(x) ) and neither is it equal to the negative of ( f(x) ). Therefore, the function ( f(x) = 1 - x^{1/3} ) does not satisfy the conditions for even or odd functions. In other words, it is neither even nor odd.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the inverse of #y=log_(1/2) x#?
- What are some common mistakes students make with function composition?
- How do you find the slant asymptote of #(x^2) / (x+1)#?
- Let # f(x) = 4x -3# and #g(f(x)) = 1/(4x)#, how do you find g(x)?
- Given the piecewise function #y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4#, how do you find the domain?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7