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
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)=
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.
Similar Questions
If f(x) is an even function and g(x) is an odd function, which of the following must be even?I. f(g(x))II. f(x) + g(x)III. f(x)g(x)A.I onlyB.II onlyC.I and II onlyD.II and III onlyE.
If f(x) is an odd function, which of the following must be even?A. f(x + 1)B.| f(x)|C.None of theseD.- f(x)E. f(|x - 1|)
Given that 𝑓(𝑥)={𝑥3𝑖𝑓𝑥≥0𝑥𝑖𝑓𝑥<0f(x)={ x 3 x ifif x≥0x<0 , which of the following functions is even?I. f(x)II. f(|x|)III. |f(x)|A.I onlyB.II onlyC.I and II onlyD.I and III onlyE.None of these
Suppose you're given the following table of values for the function f(x), and you're told that the function is even:x –2 –.35 0 .53 1f(x) 5 –3 2 2 –5Then:A.Something is wrong. Given the table of values, the function can't be even.B. f(0) + f(- .53) = 0C. f(- 1) - f(2) = - 10D. f(.35) + f(- .53) = 1E. f(2) = - 5
Which of the following is always true of odd functions?f (-x) = -f(x)f(|x|) is even|f(x)| is even
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.