Show that the function f : R rightarrow ...

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

Text Solution

AI Generated Solution

Topper's Solved these Questions

SAMPLE PAPER 2023 TERM I
CBSE MODEL PAPER|Exercise SECTION E|10 Videos

Similar Questions

Explore conceptually related problems

Show that the function f:R rarr R given by f(x)=cos x function f:R, is neither one-one nor onto.

Show that the function f:R rarr R given by f(x)=cos x for all x in R, is neither one- one nor onto

Show that the function f:R rarr R:f(x)={1 if x is rational and -1, if x is irrational is many- one into

Show that function f:R rarr{x in R:-1

Show that the function f : R to R : f(x) =3-4 x is one-one onto and hence bijective.

Show that the function f:R rarr R:f(x)=sin x is neither one-one nor onto

Show that the function f:R rarr R defined by f(x)= absx is neither one one nor onto

Show that the function f:R rarr R given by is injective.

Show that the function f:R-{3}rarr R-{1} given by f(x)=(x-2)/(x-3) is a bijection.

CBSE MODEL PAPER-SAMPLE PAPER 2024-Question

Make a rough sketch of the region {( x, y) : 0 le y le x^2 + 1, 0 le y...
Text Solution
|
Let N be the set of all natural numbers and let R be a relation on Nxx...
Text Solution
|
Show that the function f : R rightarrow {x in R : -1 < x < 1} defined ...
Text Solution
|
Solve the following system of equations using matrix method: 2/x + 3...
Text Solution
|
Find the coordinates of the image of the point (1, 6, 3) with respect ...
Text Solution
|
An aeroplane is flying along the line vec r = lambda (hat i - hat j + ...
Text Solution
|
Read the following passage and answer the questions given below: In ...
Text Solution
|
Read the following passage and answer the questions given below: In ...
Text Solution
|
Read the following passage and answer the questions given below: In ...
Text Solution
|
Read the following passage and answer the questions given below: In ...
Text Solution
|
Read the following passage and answer the questions given below: Tea...
Text Solution
|
Read the following passage and answer the questions given below: Tea...
Text Solution
|
Read the following passage and answer the questions given below: Tea...
Text Solution
|
Read the following passage and answer the questions given below: Tea...
Text Solution
|
Read the following passage and answer the questions given below: The...
Text Solution
|
If A = [a(ij)] is a square matrix of order 2 such that a(ij) ={(1," wh...
Text Solution
|
If A and B are invertible square matrices of the same order, then whic...
Text Solution
|
If the area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq...
Text Solution
|
Determine the value of the constant 'k' so that the function f(x)={((k...
Text Solution
|
The lines vec r = hat i + hat j - hat k + lambda (2 hat i+ 3 hat j - 6...
Text Solution
|