Show that the function `f : R to R {x in R : -1 lt x lt 1}` defined by `f (x) = (x)/(1 + |x|), x in R` is one one and onto function.

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

Verify whether the function f : A to B , where A = R - {3} and B = R -{1}, defined by f(x) = (x -2)/(x -3) is one-one and onto or not. Give reason.

The inverse of function f:R rarr { x in R : x lt 1} given by f(x) = (e^x-e^-x)/(e^x+e^-x) is

Show that the function f : R to R defined by f(x) = x^(2) AA x in R is neither injective nor subjective.

Let f: R to R be defined by f(x) = x^(4) , then

Let f : R to R be defined by f(x)=x^(4) , then

Show that the signum function f : R to R given by f(x) = {(1, if, x gt 0),(0, if, x = 0),(-1, if, x lt 0):} is neither one-one nor onto.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Show that the function f : R to R , defined by f(x) = 1/x is one-one and onto, where R, is the set of all non-zero real numbers.

Prove that the function f : R to R defined by f(x) = 2x , AA x in R is bijective.