If `f(x)=5xxfNtoN` then state whether f is injective or not.

If f:[0,oo[vecR is the function defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2), then check whether f(x) is injective or not.

(i) Find whether f(x)=x+cosx is one-one. (ii) Identify whether the function f(x)=-x^(3)+3x^(2)-2x+4 for f:RtoR is ONTO or INTO (iii) f(x)=x^(2)-2x,[0,3]toA . Find whether f(x) is injective or not. Also find the set A if f(x) is surjective

Let A={1,2,3},\ B={4,5,6,7} and let f={(1,4),\ (2,5),\ (3,6)} be a function from A to B . State whether f is one-one or not.

Let A}x :-1lt=xlt=1}a n df: Avec A such that f(x)=x|x|, then f is (a) bijection (b) injective but not surjective Surjective but not injective (d) neither injective nor surjective

Let A{x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is (a) bijection (b) injective but not surjective (c)Surjective but not injective (d) neither injective nor surjective

Let A = {1, 2, 5, 7}, B = {3, 4, 5, 6, 7} Let f : A rarr B be defined by f(1) = 3, f(2) = 4,f(2) = 6, f(5) = 5, f(7) = 5. Check whether f : A rarr B is a function or not.

If f(x) is an even function, then write whether f^(prime)(x) is even or odd.

If f(x) is an odd function, then write whether f^(prime)(x) is even or odd.

If f: R to R is defined by f(x) = x^(2)+1 , then show that f is not an injection.

If g(x) is a decreasing function on R and f(x)=tan^(-1){g(x)} . State whether f(x) is increasing or decreasing on R .