Question
Determine if the function is even, odd or neither.
f(x)=x^3-x^2-8x+4
f(x)=x^3-x^2-8x+4
Answers
MathMate
If the function is even,
f(x)=f(-x) for all values of x.
Likewise if the function is odd, f(x)=-f(-x) for all x.
Otherwise, it is neither.
For example,
g(x)=x²
g(-x)=(-x)²=x²
therefore g(x) is even.
h(x)=sin(x)
h(-x)=sin(-x)=-sin(x)
therefore h(x) is odd.
f(x)=f(-x) for all values of x.
Likewise if the function is odd, f(x)=-f(-x) for all x.
Otherwise, it is neither.
For example,
g(x)=x²
g(-x)=(-x)²=x²
therefore g(x) is even.
h(x)=sin(x)
h(-x)=sin(-x)=-sin(x)
therefore h(x) is odd.