CATAlgebra > Medium−12,12-\dfrac{1}{2}, \dfrac{1}{2}−21,21, and 111−1,12-1, \dfrac{1}{2}−1,21, and 11112\dfrac{1}{2}21, and 11112,1\dfrac{1}{2}, 121,1, and 32\dfrac{3}{2}23✅ Correct Option: 2Related questions:2025 Slot 3For real values of xxx, the range of the function f(x)=2x−32x2+4x−6f(x)=\frac{2x-3}{2x^2+4x-6}f(x)=2x2+4x−62x−3 isCAT 2024 Slot 1Consider two sets A={2,3,5,7,11,13}A = \{2, 3, 5, 7, 11, 13\}A={2,3,5,7,11,13} and B={1,8,27}B = \{1, 8, 27\}B={1,8,27}. Let fff be a function from AAA to BBB such that for every element bbb in BBB, there is at least one element aaa in AAA such that f(a)=bf(a) = bf(a)=b. Then, the total number of such functions fff isCAT 2024 Slot 2A function fff maps the set of natural numbers to whole numbers, such that f(xy)=f(x)f(y)+f(x)+f(y)f (xy) = f (x) f (y) + f (x) + f (y)f(xy)=f(x)f(y)+f(x)+f(y) for all x,yx, yx,y and f(p)=1f (p) = 1f(p)=1 for every prime number ppp. Then, the value of f(160000)f (160000)f(160000) is