हिंदी

Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective: k(x) = x2 - Mathematics

Advertisements
Advertisements

प्रश्न

Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

k(x) = x2 

योग
Advertisements

उत्तर

Given, A = [–1, 1]

Let k(x1) = k(x2)

x12 = x22

x1 = ± x2

Therefore, k(x) is not one-one.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ १२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 21. (iv) | पृष्ठ १२

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Let f : N → N be defined by f(n) = `{((n+1)/2", if n is odd"),(n/2", if n is even"):}` for all n ∈ N.

State whether the function f is bijective. Justify your answer.


Show that the function f : R → {x ∈ R : −1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.


Show that the function f : R → R given by f(x) = x3 is injective.


Give an example of a function which is neither one-one nor onto ?


Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x3


Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(ab) : a is a person, b is an ancestor of a


Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.


Suppose f1 and f2 are non-zero one-one functions from R to R. Is `f_1 / f^2` necessarily one - one? Justify your answer. Here,`f_1/f_2 : R → R   is   given   by   (f_1/f_2) (x) = (f_1(x))/(f_2 (x))  for all  x in R .`


Let A = {abc}, B = {u vw} and let f and g be two functions from A to B and from B to A, respectively, defined as :
f = {(av), (bu), (cw)}, g = {(ub), (va), (wc)}.
Show that f and g both are bijections and find fog and gof.


Consider f : N → Ng : N → N and h : N → R defined as f(x) = 2xg(y) = 3y + 4 and h(z) = sin z for all xyz ∈ N. Show that ho (gof) = (hogof.


 Find fog and gof  if  : f (x) = ex g(x) = loge x .


If f(x) = |x|, prove that fof = f.


 If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).


If f : R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1(24) and f−1 (5).


Which one of the following graphs represents a function?


If A = {abc} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.


Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.


Write the domain of the real function

`f (x) = sqrtx - [x] .`


Write the domain of the real function

`f (x) = sqrt([x] - x) .`


What is the range of the function

`f (x) = ([x - 1])/(x -1) ?`


If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]


\[f : R \to R \text{given by} f\left( x \right) = x + \sqrt{x^2} \text{ is }\]

 

 


Which of the following functions from

\[A = \left\{ x : - 1 \leq x \leq 1 \right\}\]

to itself are bijections?

 

 

 


If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =

 

 


Let

\[f : R \to R\]  be a function defined by

\[f\left( x \right) = \frac{e^{|x|} - e^{- x}}{e^x + e^{- x}} . \text{Then},\]
 

The function \[f : R \to R\] defined by

\[f\left( x \right) = 6^x + 6^{|x|}\] is 

 


Let

 \[A = \left\{ x \in R : x \geq 1 \right\}\] The inverse of the function, 

\[f : A \to A\] given by

\[f\left( x \right) = 2^{x \left( x - 1 \right)} , is\]

 


If  \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to


For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.


If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.


Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.


The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.


Let f : R → R be defind by f(x) = `1/"x"  AA  "x" in "R".` Then f is ____________.


Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, is ____________.


Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

  • Let f: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 is ____________.

A function f: x → y is/are called onto (or surjective) if x under f.


Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are


Let f: R→R be a continuous function such that f(x) + f(x + 1) = 2, for all x ∈ R. If I1 = `int_0^8f(x)dx` and I2 = `int_(-1)^3f(x)dx`, then the value of I1 + 2I2 is equal to ______.


If log102 = 0.3010.log103 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is ______.


Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×