To determine if the function f(x) = x^4 + x^3 is an even function, you need to check the condition for evenness. A function is considered even if:
f(-x) = f(x) for all x in the domain of the function.
Let’s evaluate f(-x):
f(-x) = (-x)^4 + (-x)^3
This simplifies to:
f(-x) = x^4 – x^3
Now, let’s compare f(-x) with f(x):
We have f(x) = x^4 + x^3 and f(-x) = x^4 – x^3.
Since f(-x) ≠ f(x) (the terms involving x^3 have different signs), we conclude that:
The function f(x) = x^4 + x^3 is not an even function.