Question

complete parts a through d to follow the step - by - step procedure to determine if the following function is even, odd, or neither. f(x)=5x^4 - x^2 + 3. a) if f is an even function, then which of the following is true? a. f(-x)=f(x) b. f(x)=\frac{1}{f(x)} c. f(x)= - f(x) d. f(-x)= - f(x) b) if f is an odd function, then which of the following is true? a. f(x)= - f(x)

Explanation:

Step1: Recall even - function definition

An even function satisfies $f(-x)=f(x)$.

Step2: Recall odd - function definition

An odd function satisfies $f(-x)=-f(x)$.

Step3: Answer part a

For an even function, the correct condition is $f(-x)=f(x)$. So the answer for part a is A. $f(-x)=f(x)$.

Step4: Answer part b

For an odd function, the correct condition is $f(-x)=-f(x)$. So the answer for part b is D. $f(-x)=-f(x)$.

Answer:

a) A. $f(-x)=f(x)$
b) D. $f(-x)=-f(x)$