Determine the values of k,m,and n that creates an odd function for p(x)=xk-xm+n

Question

Justify your answer

Answer 1

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

Comments

I think you need to check and amend your answer: the coefficient of the middle term is m, not n!

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Thanks Rod.