- #1

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I'm in Algebra II and I was given a question that was worded like this:

*"If f(x) = x², then find f(x-y)-f(x)."*

Can someone help me? I don't really know how to solve it...

-DukeGuy123

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- Thread starter DukeGuy123
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- #1

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I'm in Algebra II and I was given a question that was worded like this:

Can someone help me? I don't really know how to solve it...

-DukeGuy123

- #2

lurflurf

Homework Helper

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f(x-y)-f(x)=(x-y)^2-x^2

one would then likely be expected to expand and simplify

one would then likely be expected to expand and simplify

- #3

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It's one of these four (it's multiple choice):

A) 2x

B) x²-2xy+y²

C) -2xy+y²

D) 2xy-y²

Thanks for your help, but I would like to get an answer that is Correct and WITH WORK.

I really don't know how to solve this.

- #4

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Which answer choice would that be? And is there a more detailed way you can explain it, because I still don't get it.

Can you show it like step-by-step or something?

- #5

lurflurf

Homework Helper

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so if you have

f(x-y)-f(x)

it gives

(x-y)

you should be able to expand (x-y)

then cancel

- #6

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^{2}

so if you have

f(x-y)-f(x)

it gives

(x-y)^{2}-x^{2}

you should be able to expand (x-y)^{2}using foil or (a+b)^{2}=a^{2}+2 a b+y^{2}

then cancel

yup! f(x) =x

if the variable inside the parentheses is something other than x, it is affected the same way that x would be as long as the function is still f, and not some other function.

- #7

Mark44

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- #8

HallsofIvy

Science Advisor

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Lurflurf Suggested you expand (x-y)

Which answer choice would that be? And is there a more detailed way you can explain it, because I still don't get it.

Can you show it like step-by-step or something?

- #9

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Lurflurf Suggested you expand (x-y)^{2}- x^{2}. Have you done that yet?

in case you didnt know (x-y)^2 is really (x-y)(x-y)

with that knowledge you should be able to solve (x-y)(x-y) -x^2 just foil it all out!

(x^2-xy-xy+y^2)-x^2

combine like terms (x^2-2xy-y^2)-x^2

the x'2s cancel oiut leaving you with -2xy-y^2

factor out a -y -y(2x+y)

if i didnt totally screw this up there's your answer.

- #10

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ah ok hear x2(x-y)-x2(x)-------x3-xy-x3=xy

you dont multiply x-y times x squared. x-y IS x in this problem times the whole thing squared. thats what f(x)=x^2 is saying. its defining the function/ you did not substitute for x you just multiplied numbers by sx.

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