`(|x|-1)/(|x|-2)>=0` , ` x in bbb"R"` , `x != 2`

Solve: (|x|-1)/(|x|-2)>=0,x in R,x!=+-2

Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ne 0), (k, x = 0):} is continuous at 0.

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If f: R->R is defined by f(x)={(x+2)/(x^2+3x+2) if x in R-{-1,-2}, -1 if x = -2 and 0 if x=-1. ifx=-2 then is continuous on the set

If f : R to R is defined by f (x) = {:{((x+2)/(x^(2)+3x+2), if x in R - { 1,-2}), ( -1, if x = -2) , ( 0 , if x = -1 ) :} then f is continuous on the set

If f : R rarr R is defined by f(x) = {((x+2)/(x^(2)+3x+2), x in R-{-1,-2}),(-1, x=-2),(0, x = -1):} then f is continuous on the set