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.`

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1)>f(x_2)a n dg(x_1) f(g(3alpha-4))

Given that h(x) =f^(@) g(x) , fill in the table for h (x)

Show that the function f:N to N defined by f(x)=2x-1 is one-one but not onto.

The function f:R->[-1/2,1/2] defined as f(x)=x/(1+x^2) is

If A={-2,-1,0,1,2} and f:A to B is an onto function defined by f(x)=x^(2) +x+1 then find B .

Let f, g, h be three functions from R to R defined by f(x)=x+3, g(x) = 2x^(2) ,h(x) = 3x +1. Show that (fog)oh=fo(goh).

Let f be a twice differentiable function such that f''(x)gt 0 AA x in R . Let h(x) is defined by h(x)=f(sin^(2)x)+f(cos^(2)x) where |x|lt (pi)/(2) . The number of critical points of h(x) are

Let f:R->R and g:R->R be two one-one and onto functions such that they are mirror images of each other about the line y=a . If h(x)=f(x)+g(x) , then h(x) is (A) one-one onto (B) one-one into (D) many-one into (C) many-one onto

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1,t h e n[f(x)]^(g(x)) is increasing.