If `X={1,2,3,4},` then one-one onto mappings `f:X to X` such that `f(1)=1, f(2) ne 2 f(4) ne 4` are given by

Let X={1,2,3,4} , then one-one onto mappings f:XtoX such that f(1)=1,f(2)ne2andf(4)ne4 are given by :

Show that if f_(1) and f_(2) are one-one maps from R to R, then the product f_(1)xx f_(2):R rarr R defined by (f_(1)xx f_(2))(x)=f_(1)(x)f_(2)(x) need not be one-one.

If 2f(x) - 3f(1/x) = x^2 (x ne 0) , then find f(2).

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. A function f(x) is said to be one-one iff :

If f (x) = 1/(2x+1), x ne -1/2 , then show that , f(f (x)) = (2x+1)/(2x+3), x ne -3/2 .

Show that if f_1 and f_2 are one-one maps from r to R, then the product. f_1 xx f_2: R rarr R defined by (f_1xx f_2) (x) = f_1 (x) xx f_2(x) need not be one-one.