- #1

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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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- Thread starter caprija
- Start date

- #1

- 34

- 0

g(x) = f(x + 2)

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

my attempt

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

- #2

- 15

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(Answer: f(a) = a^2 - 4a. i.e. you just plug

Now, use the same technique for f(x+2). We just plug

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.

- #3

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(Answer: f(a) = a^2 - 4a. i.e. you just plugaintowherever 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)intowherever 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

answer: x^2 + 4

- #4

- 20

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Ok so the solution would be:

(x + 2) ^2 - 4x

x^2 + 4x - 4X + 4

answer: x^2 + 4

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

- #5

Alkatran

Science Advisor

Homework Helper

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- #6

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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)

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