Let `f(x)=(x^2+3x+a)/(x^2+x+1)` where `f:R->R`. Find the value of parameter a' so that the given function is one-one

Let f(x) = (x[x])/(x^2+1) : (1, 3) rarr R then range of f(x) is (where [ . ] denotes greatest integer function

Let f" [1,2] to (-oo,oo) be given by f(x)=(x^(4)+3x^(2)+1)/(x^(2)+1) then find value of in [f_(max)]" in "[-1,2] where [.] is greatest integer function :

Let f: R to R be defined as f(x) = e^("sgn "x)+ e^(x^(2)) . Then find the range of the function, and also indentify the type of the function : one-one or many-one.

Let f(x) = (x[x])/(x^2+1) : (1, 3) rarr R then range of f(x) is (where [ . ] denotes greatest integer function)

f : R -> R , where f(x)=(x^2+ax+1)/(x^2+x+1) Complete set of values of 'a' such that f (x) is onto, is

If f(x) = x^3 + 3x^2 + 12x - 2 sin x, where f: R rarr R, then (A) f(x) is many-one and onto (B) f(x) is one-one and onto(C) f(x) is one-one and into (D) f(x) is many-one and into

Show that f: [-1, 1] ->R , given by f(x)=x/((x+2) is one- one . Find the inverse of the function f: [-1, 1]→ S where S is the Range of f.

Let f(x)=x^2-2x-1 AA xinR Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into (3) one-one and onto (4) one- one and into

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3] , then the value of (m^(2)+n^(2))/(4) is ….