How to determine whether f(x) = x3 + 5x + 1 is an even function?
Functions are very important concepts that are extensively used in calculus and algebra. There are many types of functions, among which even and odd functions are included. Let's see how to determine if a function is even or not.
Answer: To determine whether f(x) = x3 + 5x + 1 is an even function, we will check if f(-x) = (-x)3 + 5(-x) + 1 is equivalent to f(x) = x3 + 5x + 1.
Let's understand the solution in detail.
To check whether a function is even, we check if f(-x) = f(x).
For example, for cos x, we see that cos (-x) = cos x; hence the above condition holds true. Hence it is even.
Now, for the given function, we check the above condition.
⇒ f(x) = x3 + 5x + 1
⇒ f(-x) = (-x)3 + 5(-x) + 1 = -x3 - 5x + 1
We see that (-x3 - 5x + 1) is not equal to x3 + 5x + 1. Hence, f(-x) is not equal to f(x). Hence, the function isn't even.
Thus, x3 + 5x + 1 is not an even function.