CATAlgebra > Medium(−∞,18]∪[1,∞)\left(-\infty,\frac{1}{8}\right]\cup[1,\infty)(−∞,81]∪[1,∞)(−∞,18]∪[12,∞)\left(-\infty,\frac{1}{8}\right]\cup\left[\frac{1}{2},\infty\right)(−∞,81]∪[21,∞)(−∞,14]∪[1,∞)\left(-\infty,\frac{1}{4}\right]\cup[1,\infty)(−∞,41]∪[1,∞)(−∞,14]∪[12,∞)\left(-\infty,\frac{1}{4}\right]\cup\left[\frac{1}{2},\infty\right)(−∞,41]∪[21,∞)✅ Correct Option: 2Related questions:2025 Slot 2Let f(x)=x(2x−1)f(x) = \dfrac{x}{(2x-1)}f(x)=(2x−1)x and g(x)=x(x−1)g(x) = \dfrac{x}{(x-1)}g(x)=(x−1)x. Then, the domain of the function h(x)=f(g(x))+g(f(x))h(x) = f(g(x)) + g(f(x))h(x)=f(g(x))+g(f(x)) is all real numbers except2025 Slot 1Let 3≤x≤63 \leq x \leq 63≤x≤6 and [x2]=[x]2[x^2] = [x]^2[x2]=[x]2, where [x][x][x] is the greatest integer not exceeding xxx. If set SSS represents all feasible values of xxx, then a possible subset of SSS isCAT 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 to