Question

Consider of function f (x) such that $(x^{2^{2019}-1}-1)f\left(x\right)=(x+1)(x^2+1)(x^4+1)(x^8+1)...(x^{2^{2018}}+1)-1$
then the value of f (2) is equal to

Answer 1

$(x^{2^{2019}}-1)f\left(x\right)=\frac{x^{2^{2019}}-1}{x-1}-1$

Put $x=2$

$\Rightarrow (2^{2^{2019}}-1)f\left(2\right)=2^{2^{2019}}-2$

$\Rightarrow (2^{2^{2019}}-2)f\left(2\right)=2(2^{2^{2019}}-2)$

$\Rightarrow f\left(2\right)=2$