Question: Which of the following functions is even?
Options:
f(x) = x^3
f(x) = x^2
f(x) = x + 1
f(x) = sin(x)
Correct Answer: f(x) = x^2
Solution:
A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.
Which of the following functions is even?
Practice Questions
Q1
Which of the following functions is even?
f(x) = x^3
f(x) = x^2
f(x) = x + 1
f(x) = sin(x)
Questions & Step-by-Step Solutions
Which of the following functions is even?
Correct Answer: f(x) = x^2
Step 1: Understand what an even function is. An even function is one where if you replace x with -x, the output remains the same. This means f(-x) = f(x).
Step 2: Identify the function you want to test. In this case, the function is f(x) = x^2.
Step 3: Calculate f(-x). Replace x in the function with -x: f(-x) = (-x)^2.
Step 4: Simplify f(-x). Since (-x)^2 = x^2, we have f(-x) = x^2.
Step 5: Compare f(-x) with f(x). We have f(-x) = x^2 and f(x) = x^2.
Step 6: Since f(-x) = f(x), we conclude that the function f(x) = x^2 is even.
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