Let f(x) be an decreasing function defined on `(0,oo)`. If `f(3a^2-4a+1)gtf(2a^2+a+1)` and the range of a is `(o,K/3)uu(K,K+4)`, find K

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f''(1/4) = 0 . Then (a) f'(x) vanishes at least twice on [0,1] (b) f'(1/2)=0 (c) ∫_{-1/2}^{1/2}f(x+1/2)sinxdx=0 (d) ∫_{0}^{1/2}f(t)e^sinxtdt=∫_{1/2}^{1}f(1−t)e^sinπtdt

Let f : R to R be defined as f(x) = (x^2-x+4)/(x^2+x+4) . Then the range of the function f(x) is

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)

Let f:RtoR be defined as f(x)=(x^(2)-x+4)/(x^(2)+x+4) . Then the range of the function f(x) is

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let A = {0,1,2,3,4} and f:A to ZZ be defined by f(x) = x^2 -5x+2, find the range of f.

Let f:RR to RR be defined as f(x)=(x^2-x+4)/(x^2+x+4). Then the range of the function f(x) is____

Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is a positive decreasing function, then the set of values of k for which the major axis is the x-axis is (-3,2)dot the set of values of k for which the major axis is the y-axis is (-oo,2)dot the set of values of k for which the major axis is the y-axis is (-oo,-3)uu(2,oo) the set of values of k for which the major axis is the y-axis is (-3,-oo,)

Let f:(-1,1) to R be a function defined by f(x)="max"{-|x|, -sqrt(1-x^(2))} . If K be the set of all points at which f is not differentiable, then K has exactly :