Given #f(x)= x^2/(x+2)# how do you find #f(x-2)#?
When working function problems, it's all in the substitution!
We are starting with
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
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
Let's see - we substitute just like above:
See? Everywhere there was an x, there is now x-2. Let's simplify this expression:
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