Consider the function `g(x)` defined as `g(x),(x^((2^(2011)-1))-1)=(x+1)(x^(2)+1)(x^(4)+1)……….(x^(2^(2010))+1)-1(|x|!=1)`. Then the value of `g(2)` is equal to

Options

A. `1`
B. ` 2 ^(2020)-1 `
C. `2 ^(2020)`
D. `2`

Answer

B

Explanation

`(x+1)(x^(2) +1)(x^(4)+1)….(x^(2020)+1)-1`
`=(1)/((x-1)){(x-1)(x+1)(x^(2) +1)(x^(4)+1)….(x^(2020)+1)}-1`
`=(1)/((x-1)){(x^((2020)^(2))-1)}-1=(x^(4040)x)/(x-1)`
`therefore g(x) = (x^(4040)-x)/(x-1) xx (1)/(x^(4039)-1)=(x)/(x-1)`
`rArr g(2) = 2`