A polynomial f(x) satisfies the equation f(x)+(x+1)3=2f(x+1). Find f(10).

that is (x+1) whole cube

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

Transpose the two, and switch sides
f(x+1)=(x+1)³/2
Since x+1 is the argument of the function, we replace y=x+1 and express the right-hand side in terms of y:
f(y)=y³/2
Therefore:
f(10)=10³/2

answer is wrong

Does

(x+1)3
stand for
(x+1)³
or
3(x+1)
?

x+1 whole cube

but now i got the answer
thanks..

Bhosdi ke madar...points ke liye mar rha hai!!

To find the value of f(10), we need to solve the given equation and substitute x = 10 into the function.

Let's start by simplifying the equation using the expansion for (x+1)^3.

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

Expanding (x+1)^3:
f(x) + (x^3 + 3x^2 + 3x + 1) = 2f(x+1)

Now, let's substitute x = 9 into the equation (since we want to find f(10), which means x = 10).
f(9) + (9^3 + 3*9^2 + 3*9 + 1) = 2f(10)

Simplifying the equation:
f(9) + (729 + 243 + 27 + 1) = 2f(10)
f(9) + 1000 = 2f(10)

To find f(10), we need to find the value of f(9). However, the given equation is not sufficient to determine the exact values of the polynomial.

Without any additional information about the polynomial f(x), we are unable to calculate f(10) with certainty.