हिंदी

Let f: R → R be the function defined by f(x) = 4x – 3 ∀ x ∈ R. Then write f–1

Advertisements
Advertisements

प्रश्न

Let f: R → R be the function defined by f(x) = 4x – 3 ∀ x ∈ R. Then write f–1 

योग
Advertisements

उत्तर

Given that f(x) = 4x – 3 = y (say), then

4x = y + 3

⇒ x = `(y + 3)/4`

Hence f–1(y) = `(y + 3)/4`

⇒  f–1(x) = `(x + 3)/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ ४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 6 | पृष्ठ ४

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.


Let fR → be defined as f(x) = 10x + 7. Find the function gR → R such that g o f = f o = 1R.


Give an example of a function which is not one-one but onto ?


Which of the following functions from A to B are one-one and onto?
 f1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 1 + x2


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = `x/(x^2 +1)`


If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.


If f : R → R be the function defined by f(x) = 4x3 + 7, show that f is a bijection.


If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:
(i) an injective map from A to B
(ii) a mapping from A to B which is not injective
(iii) a mapping from A to B.


Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + 3 and  g(x) = x2 + 5 .


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.


If f(x) = |x|, prove that fof = f.


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).


Consider the function f : R→  [-9 , ∞ ]given by f(x) = 5x2 + 6x - 9. Prove that f is invertible with -1 (y) = `(sqrt(54 + 5y) -3)/5`             [CBSE 2015]


If f : C → C is defined by f(x) = x2, write f−1 (−4). Here, C denotes the set of all complex numbers.


Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.


Let f be an invertible real function. Write ( f-1  of ) (1) + ( f-1  of ) (2) +..... +( f-1 of ) (100 )


Write the domain of the real function

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


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


Let

\[A = \left\{ x : - 1 \leq x \leq 1 \right\} \text{and} f : A \to \text{A such that f}\left( x \right) = x|x|\]

 


The  function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is

 


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]

 


The distinct linear functions that map [−1, 1] onto [0, 2] are


Let 
\[f : R \to R\]  be given by \[f\left( x \right) = x^2 - 3\] Then, \[f^{- 1}\] is given by 

 


Mark the correct alternative in the following question:

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


Mark the correct alternative in the following question:
Let f :  \[-\] \[\left\{ \frac{3}{5} \right\}\] \[\to\]  R be defined by f(x) = \[\frac{3x + 2}{5x - 3}\] Then,

 


Write about strcmp() function.


If A = {a, b, c, d} and f = {a, b), (b, d), (c, a), (d, c)}, show that f is one-one from A onto A. Find f–1


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


Let A = R – {3}, B = R – {1}. Let f: A → B be defined by f(x) = `(x - 2)/(x - 3)` ∀ x ∈ A . Then show that f is bijective.


Let g(x) = x2 – 4x – 5, then ____________.


The domain of the function `"f"("x") = 1/(sqrt ({"sin x"} + {"sin" ( pi + "x")}))` where {.} denotes fractional part, is


Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • The function f: R → R defined by f(x) = x − 4 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 ____________.

The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.


Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` 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 ______.


Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×