Final answer:
Substitute x-2 into f(x) to get f(x-2) = 2 - (x - 2), which simplifies to f(x-2) = 4 - x. This is the simplified polynomial of the function.
Step-by-step explanation:
To find the expression for f(x-2) given the function f(x)=2-x, we simply substitute (x-2) into the function in place of x. Therefore, we replace every x in the function with (x-2).
Following the substitution, we get:
f(x-2) = 2 - (x - 2).
Now, we simplify the expression by distributing the negative sign inside the parentheses:
f(x-2) = 2 - x + 2.
Combining like terms, we add the constant terms 2 and 2 together:
f(x-2) = 4 - x.
This result is a simplified polynomial, and there is no further simplification possible. Therefore, the answer is f(x-2) = 4 - x.