Let f : R → R be the function with formula f(x) = x 3−x 2 = x 2 (x−1). (i) Graph this function (figure out where it is zero, positive and negative). (ii) (a) Find (nonempty) sets X, Y ⊂ R so that the restriction f|X is a bijection from X onto Y . (b) Is there a maximal choice for X? i. e. is there a set X with this property and also such that no set larger that X has this property? If there is, is it unique? (c) Is there a maximal choice for Y ? If there is, is that unique?

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step-by-step explanation:

answer: x=60

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

      = x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function