Let f(x)=2x^2-x+1. Find:

F(x-1) + f(x+1)

I am not sure how to set up problem.

f(x-1)=2(x-1)^2-(x-1)+1

expand that out.
f(x+1)=2(x+1)^2-(x+1)+1
exand that out

now, add.

Thanks so much. Got it!

To find F(x-1) + f(x+1), we first need to understand what F(x-1) and f(x+1) represent.

The given function is f(x) = 2x^2 - x + 1. This means that when we input a value x into the function, we get the output 2x^2 - x + 1.

F(x-1) represents applying the function F to the input (x-1). We don't know what the function F(x) is, so we cannot directly substitute (x-1) into F. However, we can still perform the operation F(x-1) without knowing F(x) explicitly.

Similarly, f(x+1) represents applying the function f to the input (x+1). Using the given function f(x) = 2x^2 - x + 1, we can substitute (x+1) into f(x) to find the value of f(x+1).

Let's substitute (x-1) into F(x):
F(x-1) = F((x-1)).

Now let's substitute (x+1) into f(x):
f(x+1) = 2(x+1)^2 - (x+1) + 1.

Now we can write the expression F(x-1) + f(x+1) as:
F((x-1)) + 2(x+1)^2 - (x+1) + 1.

Please note that without knowing the explicit form of the function F(x), we cannot simplify this any further. The given question does not provide more information about F(x), so we cannot solve for F(x-1) + f(x+1) with the given information.