Which of the following is an even function? a. f(x) = 3x2-4x+1 b. f(x) =ex c. f(x) =3x2 -2 d. f(x)=
Question
Solution
An even function is defined as a function that satisfies the condition f(x) = f(-x) for all x in the function's domain.
Let's check each function:
a. f(x) = 3x^2 - 4x + 1 f(-x) = 3(-x)^2 - 4(-x) + 1 = 3x^2 + 4x + 1 Since f(x) ≠ f(-x), this function is not even.
b. f(x) = e^x f(-x) = e^-x Since f(x) ≠ f(-x), this function is not even.
c. f(x) = 3x^2 - 2 f(-x) = 3(-x)^2 - 2 = 3x^2 - 2 Since f(x) = f(-x), this function is even.
d. f(x) = You didn't provide a function for d.
So, the only even function among the given options is c. f(x) = 3x^2 - 2.
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