If `f(x)=cot^-1 x ; R^+ -> (0,pi/2) and g(x)=2x-x^2 ; R-> R` . Then the range of the function `f(g(x)) ` where verdefined is

f(x) = cot^(-1)x: R^(+) rarr (0,pi) and g(x) = 2x-x^(2): R rarrR then the range of f(g(x)) is ...........

The range of the function f(x)=(x^(2)-x+1)/(x^(2)+x+1) where x in R, is

The range of the function f(x) = (x^2 -x+1)/(x^2 +x+1) where x in R , is

Let f :R to R be fefined as f(x) = 2x -1 and g : R - {1} to R be defined as g(x) = (x-1/2)/(x-1) Then the composition function ƒ(g(x)) is :

If f(x)=ln(x^(2)-x+2);R^(+)rarr R and g(x)={x}+1;[1,2]rarr[1,2], Find the domain and range of f(g(x)) when defined.

If the function f and g are defined as f(x)=e^(x) and g(x)=3x-2, where f:R rarr R and g:R rarr R , find the function fog and gof.

"If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x^(2)-1,g(x)=sqrt(x^(2)+1)and h(x)={{:(,0,x le0),(,x,xgt 0):} Then the composite functions (ho fog) (x)) is given by

If f : R -> R is defined by f(x) = [2x] - 2[x] for x in R , where [x] is the greatest integer not exceeding x, then the range of f is

Let F(x) = f(x) +g(x) , G(x) = f(x) - g( x) and H(x) =(f( x))/( g(x)) where f(x) = 1- 2 sin ^(2) x and g(x) =cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following If the solution of F(x) -G (x) =0 are x_1,x_2, x_3 --------- x_n Where x in [0,5 pi] then

Let f : R^+ ->R be defined as f(x)= x^2-x +2 and g : [1, 2]->[1,2] be defined as g(x) = [x]+1. Where [.] Fractional part function. If the domain and range of f(g(x)) are [a, b] and [c, d) then find the value of b/a + d/c.