# Simple question on polynomials

If f(x)=x^2 - 4x, determine an expression for g(x)

g(x) = f(x + 2)

How would I substitute f(x) when they are separated?

my attempt

g(x) = x^2 - 4x (x + 2)

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OK, first are you happy with this one: we have f(x) = x^2 - 4x, what is f(a)?
(Answer: f(a) = a^2 - 4a. i.e. you just plug a into wherever x used to appear. It does NOT mean "f(a) = f(x) * a", which is similar to what you seem to have done in your attempt.)

Now, use the same technique for f(x+2). We just plug (x+2) into wherever x used to appear. What do you reckon the answer should be?

Once you have written f(x+2) as a polynomial, then we can call it g(x), or h(x) or y(x). So the "g(x) = " bit isn't that important.

OK, first are you happy with this one: we have f(x) = x^2 - 4x, what is f(a)?
(Answer: f(a) = a^2 - 4a. i.e. you just plug a into wherever x used to appear. It does NOT mean "f(a) = f(x) * a", which is similar to what you seem to have done in your attempt.)

Now, use the same technique for f(x+2). We just plug (x+2) into wherever x used to appear. What do you reckon the answer should be?

Once you have written f(x+2) as a polynomial, then we can call it g(x), or h(x) or y(x). So the "g(x) = " bit isn't that important.
Ok so the solution would be:

(x + 2) ^2 - 4x
x^2 + 4x - 4X + 4

Ok so the solution would be:

(x + 2) ^2 - 4x
x^2 + 4x - 4X + 4

Almost. You skipped substituting (x+2) in for one of your x's.

Alkatran
Homework Helper
It will be a lot easier if you use "a+2" instead of "x+2" then switch it back so you know you swapped them all. Much harder to make a mistake.

f(x)=x^2 -4x

f(2) = 2^2 -4*2
f(3) = 3^2 -4*3
f(m) = m^2 -4*m
whatever is inside those parenthesis next to f, you're going to substitute for every x inside the original function.

f( ) = ^2 -4* What helps sometimes is to just put in parenthesis where x is, then go back and fill them in...

(____)^2 - 4*(____)

Then, put into those parenthesis whatever is f(HERE)