CATAlgebra > Medium22213\frac{1}{3}3166623\frac{2}{3}32✅ Correct Option: 1Related questions:CAT 2019 Slot 1Consider a function fff satisfying f(x+y)=f(x)f(y)f(\mathrm{x}+\mathrm{y})=f(\mathrm{x}) \mathrm{f}(\mathrm{y})f(x+y)=f(x)f(y) where x,yx , yx,y are positive integers, and f(1)=2f(1)=2f(1)=2. If f(a+1)+f(a+2)+……+f(a+n)=f(\mathrm{a}+1)+f(\mathrm{a}+2)+\ldots \ldots+f(\mathrm{a}+\mathrm{n})=f(a+1)+f(a+2)+……+f(a+n)= 16(2n−1)16\left(2^{n}-1\right)16(2n−1) then a is equal toCAT 2021 Slot 2For all real values of x, the range of the function f(x) = x2+2x+42x2+4x+9\frac{x^2+2x+4}{2x^2+4x+9}2x2+4x+9x2+2x+4 isCAT 2024 Slot 3For any non-zero real number x, let f(x)+2f(1x)=3xf(x) + 2 f(\frac{1}{x}) = 3xf(x)+2f(x1)=3x. Then, the sum of all possible values of xxx for which f(x)=3f(x) = 3f(x)=3, is