Question

Determine whether the function f(x) = 2 - 7x² is even, odd, or neither.

a) Even
b) Odd
c) Neither
d) Insufficient information

Answer 1

The function f(x) = 2 - 7x² satisfies the condition for an even function, f(x) = f(-x), and does not satisfy the condition for an odd function, f(-x) = -f(x), therefore the function is even.

Step-by-step explanation:

To determine if the function f(x) = 2 - 7x² is even, odd, or neither, we can use the definitions of even and odd functions. An even function is one for which f(x) = f(-x) for all x in the domain of f. An odd function follows the property that f(-x) = -f(x) for all x. Let's check both conditions for the given function:

• For the even function condition: If we substitute -x for x, we get f(-x) = 2 - 7(-x)² = 2 - 7x², which is the same as the original function f(x). So, f(-x) = f(x), satisfying the condition for an even function.
• For the odd function condition: If the function were odd, then we would have f(-x) = -f(x) which would mean 2 - 7x² = - (2 - 7x²), but this is clearly not true. Therefore, f(x) is not an odd function.

Based on the analysis above, the function f(x) = 2 - 7x² is an even function.