Home
Class 12
MATHS
Let f: R->R be a function defined by f(x...

Let `f: R->R` be a function defined by `f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x))` . Then, `f` is a bijection (b) `f` is an injection only (c) `f` is surjection on only (d) `f` is neither an injection nor a surjection

A

f is both one - one and onto

B

f is one - one but not onto

C

f is onto but not one - one

D

f is neither one - one nor onto

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)) then --(1) f is bijection (2) f is an injection only (3) f is a surjection (4) f is neither injection nor a surjection

f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f^(-1)(x)=

The function f:RtoR defined by f(x)=e^(x) is

The inverse of the function f:Rto range of f, defined by f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x)) is

The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=sin^(-1)(3x-4x^3) is (a) bijection (b) injection but not a surjection (c) surjection but not an injection (d) neither an injection nor a surjection

If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invertible, find f^(-1)dot

If f:[0,oo[vecR is the function defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2), then check whether f(x) is injective or not.

If the function of f:R->A is given by f(x)=(e^x-e^(-|x|))/(e^x+e^(|x|)) is surjection, find A

Let f: RrarrR be defined by f(x)=(e^x-e^(-x))//2dot then find its inverse.