Solve: `(-1)/(|x|-2)geq1,w h e r ex in R ,x!=+-2.`

Solve: (|x|-1)/(|x|-2)geq0,x in R ,x!=+-2.

Solve: |x-1|+|x-2|geq4

Solve |x-1|+|x-2|geq4.

Solve sqrt(x-2)geq-1.

If F(x)a n dG(x) are even and odd extensions of the function f(x)=x|x|+"sin"|x+x e^x ,w h e r ex in (0,1),g(x)=cos|x|+x^2-x ,w h e r ex in (0,1) respectively to the interval (-1, 0)t h e nF(x)+G(x) in (-1,0) is (a). sin x+cos x+x e^(-x) (b)(sin x+cos x+x e^(-x)) (c)(sin x+cos x+x+x e^(-x)) (d)(sin x+cos x+x^2+x e^(-x))

If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/(dx) is. (a)1 (b) -1 (c) 0 (d) none of these

2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to (2x)/(1-x^2) t(2tan^(-1)x) tan(cot^(-1)(-x)-cot^(-1)(x)) "tan"(2cot^(-1)x)

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Solve : 2|x+1|^(2)-|x+1|=3 , x in R

Solve the following system of equations: 1/(2x)-1/y=-1 and 1/x+1/(2y)=9,w h e r e x!=0,y!=0.