# Given f(x)= x^2/(x+2) how do you find f(x-2)?

Substitute $x - 2$ everywhere there is an $x$ and you'll get to $f \left(x - 2\right) = {\left(x - 2\right)}^{2} / x$

#### Explanation:

When working function problems, it's all in the substitution!

We are starting with $f \left(x\right) = {x}^{2} / \left(x + 2\right)$

So each time we're given an "x", we're going to square it, then divide itself (after we add 2 to it first). It's easier to see that if we said $x = 1$ that we'd do the following:

$f \left(1\right) = {1}^{2} / \left(1 + 2\right) = \frac{1}{3}$

So - if we substitute a number into this function, we can come up with a single answer (substituting 1 generates an answer of 1/3).

What happens if we alter the rule? That is what your question is doing - instead of just dropping in any given number (i.e. "x"), we're instead going to subtract 2 from it first, then see what the answer is. What then is the general rule for substituting in $x - 2$?

Let's see - we substitute just like above:

$f \left(x - 2\right) = {\left(x - 2\right)}^{2} / \left(\left(x - 2\right) + 2\right)$

See? Everywhere there was an x, there is now x-2. Let's simplify this expression:

$f \left(x - 2\right) = {\left(x - 2\right)}^{2} / x$

And I don't think we can do much more than that. If we expand out the numerator, there will be terms without an x, so there isn't a clean way to get the x out from the denominator without it being a mess - it'd look like $x - 4 - \frac{4}{x}$ and that's just not simple at all!