Is the following function even, odd or neither? f(x)=x^3 +4x

- even f(x) = f(-x)
- both
- odd f(-x) = -f(x)
- neither

D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute x in the equation for -x.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

so the answer is D, neither even nor odd