math problem please help

Question

 Determine if the following functions are one-to-one, even,odd, periodic.

f(x)=8x⁵

please tell me the right answer so I can understand properly

Answer 1

A one to one function is a function that is always increasing or always decreasing. One to one functions have inverse. The graph of a one to one function will pass the HORIZONTAL LINE TEST.An odd function is a function that satisfies the condition: -f(-x) = f(x) an even function satisfies the condition f(x) = f(-x). A periodic function will contain sin, cos, tan or one of their related functions such as csc, sec and cot.

The function you are asking about is one to one. Graph it in your calculator and verify that it passes the horizontal line test.

The function is also odd.

-f(-x) = -8(-x)^5

= - 8 * -x^5

= 8x^5

The end result is equal to the original f(x). Therefore, it is odd.

The function is both odd and one to one.