Tuesday

October 21, 2014

October 21, 2014

Posted by **manny** on Thursday, September 13, 2007 at 1:27pm.

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!

- Math -
**Count Iblis**, Thursday, September 13, 2007 at 1:38pmA function f is odd iff

f(-x) = - f(x)

Put h(x) = f(x) + g(x) and calculate

h(-x):

h(-x) = f(-x) + g(-x) =

-f(x) - g(x) =

-[f(x) + g(x)] =

-h(x)

So, we see that h is odd because h(-x) = -h(x)

Now put h(x) = g[f(x)]

h(-x) = g[f(-x)] =

g[-f(x)] =

-g[f(x)] =

-h(x)

And we see that h is odd.

One more exercise you could do:

If f(x) is an arbitrary function show that it can be decomposed uniquely as:

f(x) = f_even(x) + f_odd(x)

where f_even and f_odd are even and odd functions, respectively. Give the expressions for these functions in terms of the function f.

- Math -
**manny**, Thursday, September 13, 2007 at 1:45pmgot it.

Thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

**Answer this Question**

**Related Questions**

odd and even functions - Using f is odd if f(-x) = -f(x) or even if f(-x) = f(x...

math - I know It's probably an easy question but I don't know remember how to do...

college algebra - Let f denote an odd function and g an odd function. Decide ...

discrete math - use a direct proof to show that the product of two odd numbers ...

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

Algebra - Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief ...

Algebra - Confused Please Help! Thanks! Let f(x) = 1 – 3x^2. Which of the ...

Algebra - Let f(x) = 1 – 3x^2. Which of the following is true? Please give us a ...

Calculus, check my answers, please? :) - Okay, so I think these are right, but I...

Algebra - Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief ...