Question

Which statement best describes how to determine whether f(x) = x4 – x3 is an even function?

(A) Determine whether (–x)4 – (–x)3 is equivalent to x4 – x3.
(B) Determine whether (–x4) – (–x3) is equivalent to x4 + x3.
(C) Determine whether (–x)4 – (–x)3 is equivalent to –(x4 – x3).
(D) Determine whether (–x4) – (–x3) is equivalent to –(x4 + x3).

Answer 1

a function is even if it can be reflected across the y axis and map onto itself

basically f(x) is even if f(-x)=f(x)

easy way to test is to see if f(-x)=f(x)


`(-x)^4-(-x)^3=x^4-x^3`

`x^4-(-x^3)=x^4-x^3`

`x^4+x^3=x^4-x^3`
nope, not even

answer is A

Answer 2

For an even function f(x) = f(-x)

So its option A