Determine the values of k,m,and n that creates an odd function for p(x)=xk-xm+n
A function f(x) is odd if -f(x) = f(-x)
Taking p(x) = xk - xm + n = x(k - m) + n
Setting -p(x) = p(-x),
-x(k - m) - n = (-x)(k - m) + n
-x(k - m) = (-x)(k - m) + 2n
Comparing the coefficients of x and the constant values
-(k - m) = -(k - m)
0 = 2n
Therefore, n = 0 and k,m take any values
Answer: p(x) = xk - m + n is odd for any values of k and m, but n must be zero