Let `f:Rrarr{-1,0,1}` be defined by `f(x)=sgn(frac{1-|x|}{1+|x|})` then f(x) is
(A) Onto
(B) Odd
(C) One- one
(D) Bijective

If f(x) = x^3 - frac{1}{x^3} then f(x)+f(1/x)= (A)2 x^3 (B) 2/x^3 (C) 0 (D) 1

Let a function f:(0,infty)to[0,infty) be defined by f(x)=abs(1-1/x) . Then f is

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

Let f: R->R^+ be defined by f(x)=a^x ,\ a >0 and a!=1 . Write f^(-1)(x) .

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:[0,5] to [-1,5] , where f(x)={x^2-1,0 then f(x) is : (A) one-one and onto (B) one-one and into (C) many one and onto (D) many one and into

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then (a) f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval