Question

given f(x)=2x-x2 find f(x+1),f(x)+f(1)​

Answer 1

Step-by-step explanation:

fx+1)= 2(x+1) - (x+1)2

= 2x+2 -2x-2

2x &2 cancelled out & we get

f(x+1)=0

f(x)+f(1) =2x-x2 +(2-2)

=2x-x2

Answer 2

Answer:

f(x+1) = 1 - x² and f(x)+f(1) = 2x-x²+1

Step-by-step explanation:

Given that

f(x) = 2x -x²

Now we have to find the values of f(x+1) and f(x)+f(1)

f(x) = 2x - x²

f(x+1) = 2(x+1) - (x+1)²

         = 2x + 2 - [x²+1+2x]

         = 2x+2-x²-1-2x

        = 1 - x²

f(1) = 2(1) - (1)² = 2 - 1 = 1

f(x) + f(1) = 2x-x²+1

Therefore, f(x+1) = 1 - x² and f(x)+f(1) = 2x-x²+1