An even function satisfies f(x) = f(-x). f(x) = x^2 is even.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following is an even function?
Solution: An even function satisfies f(x) = f(-x). f(x) = x^2 is even.
Steps: 6
Step 1: Understand what an even function is. An even function is one where the output is the same when you input a number and its negative. This means f(x) = f(-x).
Step 2: Look at the function f(x) = x^2. To check if it's even, we need to find f(-x).
Step 3: Calculate f(-x) for the function f(x) = x^2. This means replacing x 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) and f(-x). We see that f(x) = x^2 and f(-x) = x^2 are the same.
Step 6: Since f(x) = f(-x), we conclude that f(x) = x^2 is an even function.
