Question

If f(x) = x^3 - x^2 - 3, which of the following is equal to g(x) = f(2 - x)?

Answer 1

x^3 + 5x^2 - 8x + 1
-x^3 + 7x^2 - 16x - 15
x^3 + 5x^2 + 8x + 1
x^3 - 7x^2 + 16x - 15

Answer 2

None of the above!

Answer 3

Should be -x^3 + 5x^2 - 8x + 1

Answer 4

If f(x) is a third degree polynomial function and g(x) = f(-2x), which of the following is NOT true?

f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercept.
f(2) = g(-1)
f(x) and g(x) have the same number of zeros.


@mathmale

Answer 5

@CGGURUMANJUNATH

Answer 6

Ricky, Hello!
I've taken a look at this problem and have an idea of what to do, 'though I haven't actually completed all the work. I'd suggest you look at the four answer choices and decide which of them is/are true, first, and that way narrow down to which is NOT true. Have you been able to decide which are true or probably true?

Answer 7

Here's one possible approach:
Invent a 3rd order function: f(x)=2x^3 -x + 1
Substitute (-2x) for x : f(-2x)=2(-2x)^3 - (-2x) + 1 = -16x^3 + 2x + 1

Now you could find both the vertical and horizontal intercepts for both versions of the function, above, and that would enable you to accept or reject the possibilities

f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercept..

I need to get off my computer now, unfortunately. Hope this suggestion at least helps you get started with this homework problem. Best to you. MM