If `fa n dg` are two distinct linear functions defined on `R` such that they map `{-1,1]` onto `[0,2]` and `h : R-{-1,0,1}vecR` defined by `h(x)=(f(x))/(g(x)),` then show that `|h(h(x))+h(h(1/x))|> 2.`

If f,g,\ h are three functions defined from R\ to\ R as follows: the range of h(x)=x^2+1

Let f(x) be a function defined on [-2,2] such that f(x)=-1-2<=x<=0 and f(x)=x-1,0

If f,g,\ h are three functions defined from R\ to\ R as follows: Find the range of f(x)=x^2

If f(x)=(1)/(x), evaluate lim_(h rarr0)(f(x+h)-f(x))/(h)

Let A=R-{2} and B=R-{1}. If f:A rarr B is a mapping defined by f(x)=(x-1)/(x-2), show that f is bijective.

Let A=R-[2] and B=R-[1]. If f:A rarr B is a mapping defined by f(x)=(x-1)/(x-2), show that f is bijective.

If f(x)=(sin(pi x)/(4))/(x+1) , then lim_(h rarr0)(f(1+h)-f(1))/(h^(2)+2h) is

A function is said to be bijective if it is both one-one and onto, Consider the mapping f : A rarr B be defined by f(x) = (x-1)/(x-2) such that f is a bijection. Let g : R - {2} rarr R - {1} be defined by g(x) = 2f(x) - 1 . Then g(x) in terms of x is :

Let the function f(x)=x^(2)+x+sin x-cos x+log(1+|x|) be defined on the interval [0,1]. Define functions g(x) and h(x) in [-1,0] satisfying g(-x)=-f(x) and h(-x)=f(x)AA x in[0,1]