Which of the following functions is an even function?
Practice Questions
Q1
Which of the following functions is an even function?
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 an even function?
Correct Answer: f(x) = x^2
Step 1: Understand what an even function is. An even function is one where f(-x) = f(x). This means that if you plug in a negative number, the output will be the same as if you plugged in the positive version of that number.
Step 2: Look at the function given, which is f(x) = x^2. We need to check if it is an even function.
Step 3: Calculate f(-x). Replace x with -x in the function: 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 see that f(-x) = x^2 and f(x) = x^2, so f(-x) = f(x).
Step 6: Conclude that since f(-x) = f(x), the function f(x) = x^2 is an even function.
