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:CAT 2019 Slot 1For any positive integer nnn, let f(n)=n(n+1)f(n)=n(n+1)f(n)=n(n+1) if nnn is even, and f(n)=n+3f(n)=n+3f(n)=n+3 if nnn is odd. If mmm is a positive integer such that 8f(m+1)−f(m)=28 f(m+1)-f(m)=28f(m+1)−f(m)=2, then mmm equalsCAT 2022 Slot 1For any real number x, let [x] be the largest integer less than or equal to x. If ∑n=1N[15+n25]=25\sum_{n=1}^{N} [\frac{1}{5} + \frac{n}{25}] = 25∑n=1N[51+25n]=25 then N isCAT 2017 Slot 2Let f(x)=x2f(x) = x^2f(x)=x2 and g(x)=2xg(x) = 2^xg(x)=2x, for all real xxx. Then the value of f(f(g(x))+g(f(x)))f(f(g(x)) + g(f(x)))f(f(g(x))+g(f(x))) at x=1x = 1x=1 is