This exercise on the Khan Academy requires you to determine whether the following function is odd or even
f(x) = $-5x^5 - 2x - 2x^3$
To answer the question, the instructor goes through the following process
- what is f(-x)
- f(-x) = $-5(-x)^5 - 2(-x) - 2(-x)^3$
- f(-x) = $5(x)^5 +2(x) + 2(x)^3$
- f(-x) = $-(-5x^5 - 2x - 2x^3)$
- f(-x) = -f(x)
Therefore f(x) is odd.
Question. Why is everything converted to a negative both inside and outside the parenthesis at step 4?
At step 2, he's making x negative. At step 3, we get the result of making the x values negative. So why add the negatives again at step 4?