Question

Explain the following mathematical statement :-

Answer 1

Any polynomial function 'f' such that R is related to R, where 'R' is set of real numbers, is onto if degree of 'f' is odd and into if degree of 'f' is even.

Answer 2

Every polynomial of odd order crosses the origin from +infinity to -infinity. Hence they are onto. eg.x^3,x^5 etc

Every polynomial of even order is symmetrical along y axis and hence into. You can check this by the horizontal line test. eg x^2,x^4.

Answer 3

even functions are like x^0, x^2, x^4, x^2n

odd functions are like x^1, x^3, x^5, x^(2n+1)

Answer 4

Thankyou Sir