Post a New Question


posted by .

Suppose an odd function f has an inverse g. Prove that g is also odd.

  • Math -

    f(-x) = -f(x)

    x = g(y)
    -x = g(-y) but -x = -(g(y)) = -g(y)
    so, g is odd

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. discrete math

    use a direct proof to show that the product of two odd numbers is odd. Proofs: (all the nos. i used are odd) 3 x 3 = 9 5 x 9 = 45 7 x 3 = 21 Yes, but you didn't prove the statement for "all" odd integers, only the odd integers you …
  2. discrete math

    prove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start with …
  3. odd and even functions

    Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x) for all real x, how do I 1)show that a polynomial P(x) that contains only odd powers of x is an odd function 2)show that if a polynomial P(x) contains both odd and even powders …
  4. math

    I know It's probably an easy question but I don't know remember how to do it. Show the work to determine if the relation is even, odd, or neither. a ) f(x) = 2x^2 - 7 b) f(x) = -4x^3 - 2x c) f(x) = 4x^2 - 4x + 4 If f(-x) = f(x), for …
  5. Math

    Let f and g be two odd functions. Prove that: a) f + g is an odd function b) g of f is an odd function I am not even sure where to start, any help that can be provided would be appreciated!
  6. college algebra

    Let f denote an odd function and g an odd function. Decide whether the function h(x)=g(x) f(x) is even or odd.
  7. Maths

    The first odd number can be expressed as 1 = 1squared - 0squared. The second odd number can be expressed as 3 = 2squared - 1squared. The third odd number can be expressed as 5 = 3squared - 2squeared. a) Express the fourth odd number …
  8. Calculus, check my answers, please! 3

    Did I get these practice questions right?
  9. Calculus, check my answers, please? :)

    Okay, so I think these are right, but I would appreciate if someone could check them and tell me if something is wrong and what the right answer is. I'd also appreciate an explanation if possible. :)Thank you! 7. Given that f(x)={x^3 …
  10. Math

    If f and g are functions defined for all real numbers, and f is an odd function, then f ∘ g is also an odd function. Justify. I wrote false cause for example if f = x^3(odd) and g=x^2(even) the fog is even.

More Similar Questions

Post a New Question