# Simple function question

For:

f(x-1)=x+3


Find:

f(x)


I find the answer to be: f(x)=x+2. But my textbook said it's x+4. What am I doing wrong?

Update: Just found the solution in my textbook: Let's say y=x-1->x=y+1
f(y)=y+1+3=y+4

This means: f(x)=x+4 f(2)=2+4=6

Does this make sense? I'm confused.

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I can't say what you're doing wrong since I don't know what you did. But note $f(x)=f\bigl( (x+1)-1\bigr) = (x+1)+3=x+4$. – David Mitra Feb 24 '14 at 11:29
@DavidMitra your comment might be the solution.. Mind explaining it as an answer? I'm a noob in functions. – Mouse Hello Feb 24 '14 at 11:41
I just noticed it worked. Perhaps better: the graph of $y=f(x-1)$ is the graph of $y=f(x)$ shifted to the right one unit. You're told this gives $y=x+3$. So you need to take this and shift to the left one unit to get $f(x)$ back. So you replace the "$x$" with "$x+1$" to get $f(x)=(x+1)+3$. – David Mitra Feb 24 '14 at 11:44
@DavidMitra I've updated the question, take a look. What do you think? I need the answer algebraically – Mouse Hello Feb 24 '14 at 11:52

You have: $$f(x-1) = x+3 = (x-1) + 4$$
Now changing the $x-1$ into an $x$ you get : $$f(x) = x+4$$
You can write $y = x-1$ if you wish in which case you end up with $f(y) = y+4$. $x$ and $y$ are just dummy variables so the answer is good. – user88595 Feb 24 '14 at 12:10