If `x, y in R` then which one is never be a function?

Show that the function f: R rarr R defined by f(x) = (4x-3)/5, x in R is one one and onto function.

If R is the set of real numbers and a function f: R to R is defined as f(x)=x^(2), x in R , then prove that f is many-one into function.

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

If R is the set of real numbers prove that a function f:R rarr R,f(x)=e^(x),x in R is one to one mapping.

If R is the set of real numbers prove that a function f: R -> R,f(x)=e^x , x in R is one to one mapping.

Show that the function f: R rarr R defined by f(x) = (3x-1)/2, x in R is one-one and onto function.

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