Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = 3x2 - 1
We will use the concept of odd and even function to solve this.
Answer: The function f(x) = 3x2 - 1 is an even function.
Let's solve this step by step.
Given that, f(x) = 3x2 - 1
We know from the definition of odd and even functions that:
A function is an Even Function if f(-x) = f(x) for all x.
A function is an Odd Function if f(-x) = - f(x) for all x.
So, let's find f(-x) first.
Here f(x) = 3x2 - 1
So, f(-x) = 3(-x)2 - 1 = 3x2 - 1 = f(x)
Hence, f(-x) = f(x)