Question

If f(x + 2) = x-3, find f(x) and f(2x + 3)​

Answer 1

Step-by-step explanation:

Well, we know that there exists a function f(x) such that f(x−1) is a direct transformation of its parent function. First we want to set x=x−1 . Conceptually, it might be easier just to annotate one of the x ’s as a completely different variable, because we know that x doesn’t equal x−1 . So let’s rewrite as x=y−1 and solve for y .

We now have y=x+1 where y(x) is actually our parent function and y(x)=f(x+1) . So take our equation f(x−1) and substitute each x with (x+1) . So

f(x)=2(x+1)+3

and

f(x)=2x+5 .

We can check this by finding f(x−1) because it should equal 2x+3:

f(x−1)=2(x−1)+5

f(x−1)=2x+3 .