Timed Quant Practice - Medium Section 1 Sample 3 Question 2

[lisagogo]

Hi everyone, for this question below I know Greg has a different method to arrive to the solution but I was wondering if my method/ thought process is also correct or not.
Given g(x) is odd, all exponents of g(x) must be odd. However it is also given that f(x) is even, which means an odd g(x) would violate this rule and hence g(x) must be 0?

With this rationalising I believe if question asks about f(x) instead, f(x) also equates 0.

Thanks everyone, question is from Timed Quant Practice - Medium Section 1 Sample #3**.**

[cylverixxx]

@lisagogo

Given g(x) is odd, all exponents of g(x) must be odd. However it is also given that f(x) is even, which means an odd g(x) would violate this rule and hence g(x) must be 0?

Looks okay to me, but you’re assuming g(x) is a polynomial. What about the case when g isn’t a polynomial?

@lisagogo

With this rationalising I believe if question asks about f(x) instead, f(x) also equates 0.

It would be 1 going off your logic

[lisagogo]

thanks so much! I get it now.