Answer:
B.
Step-by-step explanation:
If f(-x)=f(x), then f is even.
If f(-x)=-f(x), then f is odd.
To determine if f(x)=3x^4+5x^2+1 is even or odd plug in -x like so:
f(x)=3x^4+5x^2+1
f(-x)=3(-x)^4+5(-x)^2+1
f(-x)=3x^4+5x^2+1
f(-x)=f(x)
So f is even.
You should keep in mind the following:
(-x)^odd=-(x^odd)
(-x)^even=x^even
Examples:
(-x)^81=-(x^81) since 81 is odd
(-x)^10=x^10 since 10 is even
Anyways, the student is right and f(-x)=f(x).
Answer:
The student's claim is true, because for any input of x, f(x)=f(−x).
Step-by-step explanation:
If a student says that the function f(x)=3x^4+5x^2+1 is an even function, the student's statement true because for any input of x, f(x)=f(−x).
f(-x)=f(x) is even.
f(-x)=-f(x) is odd
