Show that `vv : R xx R rarr R` given by `(a, b) rarr max. [a, b)` and `^^: R xx R rarr R` given by `(a, b) rarr min (a, b)` are binary operations.

Show that * : R xx R rarr R given by a * b rarr a + 2b is nto associative.

Show that +: R xx R rarr R and xx : R xx R rarr R are commutative binary operations.

Show that :- R xx RrarrR and div : R xx R rarrR are not commutative binary operations.

Show that the function f : R rarr R given by f (x) = x^3 is injective.

Show that the function f : R rarr R given by f(x) =x^2 is injective.

Show that f : R rarr~ gien f (X) =x^3 is bijective.

Let f : R rarr R be given byf(X) = tan x, then f^-1 (1) is

If f : R rarr R given by f(x) = x^3 + 2 , then f^-1(x) equals :

Prove that the function f: R rarr R given by: f(x) = 2x is one-one and onto.

If the formula f : R rarr R be given by f(x) = x^2 2 and g : R rarr R be given by g(x) = (x)/(x-1). X ne 1 . Find fog and gof. Hence find (fog) (2) and (gof (-3)