Let `f(x) ={x^2-4, if |x|<=3 and 5sgn|x-3|, if |x|>3` and `g(x)=2 tan^-1 (e^x)-pi/2` for all `x in R`, then which of the following is(are) correct ?

Let f(x)={x^(2)-4,quad if |x| and g(x)=2tan^(-1)(e^(x))-(pi)/(2) for all x in R, then which of the following is(are) correct?

if f(x)=|1-x|,1<=x<=2, and g(x)=f(x)+b sin((pi x)/(2)) then which of the following is correct

Let f(x)=x^(2)-3x+4;x =3 Let g(x)=x+6;x =4 then which of the following are true

Let f : I - {-1,0,1} to [-pi, pi] be defined as f(x) = 2 tan^(-1) x - tan^(-1)((2x)/(1 -x^(2))) , then which of the following statements (s) is (are) correct ?

Let f : I - {-1,0,1} to [-pi, pi] be defined as f(x) = 2 tan^(-1) x - tan^(-1)((2x)/(1 -x^(2))) , then which of the following statements (s) is (are) correct ?

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let f(x) = sin (pi/6 sin (pi/2 sinx)) for all x inR and g(x) = pi/2 sinx for all x in R . Let (fog)(x) dentoe f(g(x)) and (gof)(x) denote g(f(x)). Then which of the following is (are) True?