Question

Find f(x) if it is known that f(x−2)=2−x.

Answer 1

The function is f(x) = - x

How to find f(x)?

Replace x-2 with x:

Since we're given that f(x-2)=2-x, we can directly substitute x-2 wherever we see x in the equation. This substitution represents "shifting" the function two units to the right.

Apply the substitution:

f(x-2) = 2-x

becomes:

f(x) = 2 - (x + 2)

Combine like terms:

f(x) = 2 - x - 2

Simplify:

f(x) = -x

Therefore, f(x) = -x satisfies the given condition.

Answer 2

`\bf f(x-2)=2-x\impliedby \textit{now, let's set the value for }x=x+2 \\\\\\ f\left(\boxed{x+2}-2 \right)=2-\boxed{x+2}\implies f(x)=4-x`