#### Question:

Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x

Posted By Admin @ September 03, 2022

Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x

Try this option:

the rule: if f(-x)=f(x), then the function f(x) is even, if f(-x)=-f(x) then the function is odd.

1. f(x)=-5x⁴-2;

if to substitute x→(-x), then f(-x)=-5*(-x)⁴-2; ⇔ f(-x)=-5x⁴-2, in other words f(x)=f(-x), it means that this function is even.

2. f(x)=x³+2x.

if to substitute x→(-x), then f(-x)=(-x)³+2*(-x); ⇔ f(-x)=-(x³+2x), in other words f(-x)=-f(x), it means that this function is odd.

the rule: if f(-x)=f(x), then the function f(x) is even, if f(-x)=-f(x) then the function is odd.

1. f(x)=-5x⁴-2;

if to substitute x→(-x), then f(-x)=-5*(-x)⁴-2; ⇔ f(-x)=-5x⁴-2, in other words f(x)=f(-x), it means that this function is even.

2. f(x)=x³+2x.

if to substitute x→(-x), then f(-x)=(-x)³+2*(-x); ⇔ f(-x)=-(x³+2x), in other words f(-x)=-f(x), it means that this function is odd.

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