I have a quick question on one of the practice questions. There was an explanation offered, but I’m still confused 🙁

This is for PWN 4th Edition –> Page 100, Question 2
f(x-1) = X +1 for all values of x, which of the following is equal to f(x+1)?
The explanation in the back of the book is a bit unclear to me and I really need another way to look at this problem Any help is appreciated, thanks in advance!

Remember that one helpful way to think about functions is that they’re like a machine (in the book I use the example of the car wash) that performs the same operation on anything that gets put into it. So if you know that the function g is defined as g(x)=3x+1, then you know that g(a)=3a+1. You also know that g(x-2)=3(x-2)+1, you know that g(5)=3(5)+1, etc. In plain English, you know that whatever gets put into the function g gets multiplied by 3, and then 1 is added to the result.

In this question, we don’t know what the f function is, but we do know that when (x-1) gets put into the function, (x+1) comes out. So the question we need to answer is really this: what arithmetic operations can the function be performing on (x-1) to turn it into (x+1)?

There’s nothing the function can divide by or multiply by to get that result. There are no exponents that would produce that result.

However, there is a simple addition the function could be doing to produce that result!

What if the function is simply adding 2? That would certainly turn (x-1) into (x+1): (x-1)+2=x+1.

If the function is just adding 2, then we can write the regular f(x) thusly: f(x)=x+2. That means that whatever gets put into the function machine, 2 is added to it and nothing else happens.

Now, let’s use the definition we just figured out for f(x) to evaluate f(x+1).


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