Show that the function f : R rarr { x in...

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.

SAMPLE PAPER 4
ARIHANT PUBLICATION|Exercise Short Answer Type Questions|25 Videos
SAMPLE PAPER 3
ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS |13 Videos
SAMPLE PAPER 5
ARIHANT PUBLICATION|Exercise Long answer type question|13 Videos

Similar Questions

Explore conceptually related problems

Show that the function f: R rarr R , f(x)= x^(4) is many-one and into.

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

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

State whether the function f : R rarr R, defined by f(x) = 3 - 4x is onto or not.

Show that the function f: N rarr N, given by f(1) f(2)= 1 and f(x) = x - 1 for every x gt 2, is onto but not one-one.

Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-one nor onto.

Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neither one-one nor onto.

Show that f : R to R defined as f(x) = sgn(x) is neither one-one nor onto.

Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][x^2], xne0),(0, x=0):} is onto but not one-to-one.