Consider two functions, f(x) and g(x) defined as under: `f(x)={1+x^3,x < 0 x^2-1,x >= 0 and g(x) ={(x-1)^(1/3) (x+1)^(1/2), x < 0 x >= 0.` Evaluate g(f(x)).

If the functions of f and g are defined by f(x)=3x-4 and g(x)=2+3x then g^(-1)(f^(-1)(5))

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then minimum value of f (x) is:

Consider the function f(x) satisfyig the identity f(x)+f((x-1)/(x))=1+x,AA x in R-{0,1} and g(x)=2f(x)-x+1

If f(x) = (1)/(1 -x) x ne 1 and g(x) = (x-1)/(x) , x ne0 , then the value of g[f(x)] is :

If f(x) and g(x) are two functions with g (x) = x - 1/x and fog (x) =x^(3) -1/x^(3) then f(x) is

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

If f(x) and.g(x) are two functions with g(x)=x-(1)/(x) and f(g(x))=x^(3)-(1)/(x^(3)) then f(x) is