Determine if the function is odd, even or neither. Explain your reasoning.

Question

f(x)=x^2

g(x)=x^3

f(x)=√x

g(x)=∛x

Answer 1

f(x)=x^2

g(x)=x^3

f(x)=√x

g(x)=∛x

For a function h(x), if h(-x)=h(x), then h(x) is even. If h(-x)=-h(x), then h(x) is odd.

First one f(x)=x²

f(-x)=(-x)²=x²=f(x) so the function is even.

Second one g(x)=x^3

g(-x)=(-x)³=-x³=-g(x) so the function is odd.

Third one f(x)=√x

f(-x)= √(-x). The function is undefined for x>0. For x<0, the function is defined but f(-x)≠f(x). For example, if x=-4, f(--4)= √--4=√4=±2. The function is neither.

Fourth one g(x)=∛x

g(-x)=∛(-x)=-∛x=-g(x) so the function is odd.