हिंदी

Let S = {A, B, C} And T = {1, 2, 3}. Find F−1 Of the Following Functions F From S To T, If It Exists. F = {(A, 3), (B, 2), (C, 1)} - Mathematics

Advertisements
Advertisements

प्रश्न

Let S = {abc} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.

F = {(a, 3), (b, 2), (c, 1)} 

उत्तर

S = {abc}, T = {1, 2, 3}

F: S → T is defined as:

F = {(a, 3), (b, 2), (c, 1)}

⇒ F (a) = 3, F (b) = 2, F(c) = 1

Therefore, F−1T → S is given by

F−1 = {(3, a), (2, b), (1, c)}.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations and Functions - Exercise 1.5 [पृष्ठ ३०]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 1 Relations and Functions
Exercise 1.5 | Q 11.1 | पृष्ठ ३०

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Check the injectivity and surjectivity of the following function:

f: Z → Z given by f(x) = x2


Following the case, state whether the function is one-one, onto, or bijective. Justify your answer.

f : → R defined by f(x) = 3 − 4x


Following the case, state whether the function is one-one, onto, or bijective. Justify your answer.

f: → R defined by f(x) = 1 + x2


Let S = {abc} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.

F = {(a, 2), (b, 1), (c, 1)}


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


Classify the following function as injection, surjection or bijection :

f : Z → Z, defined by f(x) = x2 + x


Show that the logarithmic function  f : R0+ → R   given  by f (x)  loga x ,a> 0   is   a  bijection.


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


Find fog and gof  if : f (x) = x2 g(x) = cos x .


Find fog and gof  if : f(x) = sin−1 x, g(x) = x2


   if `f (x) = sqrt(1-x)` and g(x) = `log_e` x are two real functions, then describe functions fog and gof.


Let

f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`

Find fof.


State with reason whether the following functions have inverse:

h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}


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).


 If f : R → R be defined by f(x) = x4, write f−1 (1).

Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\]  be a function defined by f(x) = cos [x]. Write range (f).


Let f : R → R+ be defined by f(x) = axa > 0 and a ≠ 1. Write f−1 (x).


Let f : R → R be defined as  `f (x) = (2x - 3)/4.` write fo f-1 (1) .


Write whether f : R → R, given by `f(x) = x + sqrtx^2` is one-one, many-one, onto or into.


If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = \[\alpha x + \beta\]  then find the values of \[\alpha\] and \[ \beta\] . [NCERT EXEMPLAR]


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


The function \[f : [0, \infty ) \to \text {R given by } f\left( x \right) = \frac{x}{x + 1} is\]

 

 


The range of the function

\[f\left( x \right) =^{7 - x} P_{x - 3}\]

 


Which of the following functions form Z to itself are bijections?

 

 

 
 

If \[f : R \to R is given by f\left( x \right) = 3x - 5, then f^{- 1} \left( x \right)\] 

 


Which function is used to check whether a character is alphanumeric or not?


Write about strlen() function.


Let f: R → R be defined by f(x) = 3x – 4. Then f–1(x) is given by ______.


Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______


Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D


Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1 


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


Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.


Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is ____________.


Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is


Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not


Let [x] denote the greatest integer ≤ x, where x ∈ R. If the domain of the real valued function f(x) = `sqrt((|[x]| - 2)/(|[x]| - 3)` is (–∞, a) ∪ [b, c) ∪ [4, ∞), a < b < c, then the value of a + b + c is ______.


Let f(1, 3) `rightarrow` R be a function defined by f(x) = `(x[x])/(1 + x^2)`, where [x] denotes the greatest integer ≤ x, Then the range of f is ______.


Write the domain and range (principle value branch) of the following functions:

f(x) = tan–1 x.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×