हिंदी

Find Gof And Fog When F : R → R And G : R → R Is Defined By F(X) = 2x + X2 And G(X) = X3 - Mathematics

Advertisements
Advertisements

प्रश्न

Find gof and fog when f : R → R and g : R → R is defined by  f(x) = 2x + x2 and  g(x) = x3

उत्तर

Given, f : R → R and g : R → R
So, gof : R → R  and fog : R → R

f(x) = 2x + x2 and g(x) = x3

(gof) (x)

g (f (x))

g (2x+x2)

(2x+x2)3

(fog) (x)

f (g (x))

f (x3)

2 (x3)+(x3)2

=2x3+x6

 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Functions - Exercise 2.2 [पृष्ठ ४६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 2 Functions
Exercise 2.2 | Q 1.2 | पृष्ठ ४६

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

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


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}


 Which of the following functions from A to B are one-one and onto ?  

f3 = {(ax), (bx), (cz), (dz)} ; A = {abcd,}, B = {xyz}. 


Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.


If f : A → B and g : B → C are onto functions, show that gof is a onto function.


Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

.


Let

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

Find fof.


State with reason whether the following functions have inverse :
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}


Find f −1 if it exists : f : A → B, where A = {1, 3, 5, 7, 9}; B = {0, 1, 9, 25, 49, 81} and f(x) = x2


Let A = {1, 2, 3, 4}; B = {3, 5, 7, 9}; C = {7, 23, 47, 79} and f : A → Bg : B → C be defined as f(x) = 2x + 1 and g(x) = x2 − 2. Express (gof)−1 and f−1 og−1 as the sets of ordered pairs and verify that (gof)−1 = f−1 og−1.


Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`


Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.


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.


If f(x) = 4 −( x - 7)3 then write f-1 (x).


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

 


\[f : R \to R\] is defined by

\[f\left( x \right) = \frac{e^{x^2} - e^{- x^2}}{e^{x^2 + e^{- x^2}}} is\]

 


\[f : Z \to Z\]  be given by

 ` f (x) = {(x/2, ", if  x is even" ) ,(0 , ", if  x  is  odd "):}`

Then,  f is


The inverse of the function

\[f : R \to \left\{ x \in R : x < 1 \right\}\] given by

\[f\left( x \right) = \frac{e^x - e^{- x}}{e^x + e^{- x}}\] is 

 


Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.


Write about strlen() 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 R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.


Let A be a finite set. Then, each injective function from A into itself is not surjective.


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


Let the function f: R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto


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

k(x) = x2 


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


If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.


The smallest integer function f(x) = [x] is ____________.


Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?

Let A = {1, 2, 3, ..., 10} and f : A `rightarrow` A be defined as

f(k) = `{{:(k + 1, if k  "is odd"),(     k, if k  "is even"):}`.

Then the number of possible functions g : A `rightarrow` A such that gof = f is ______.


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

f(x) = tan–1 x.


ASSERTION (A): The relation f : {1, 2, 3, 4} `rightarrow` {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function.

REASON (R): The function f : {1, 2, 3} `rightarrow` {x, y, z, p} such that f = {(1, x), (2, y), (3, z)} is one-one.


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.



The given function f : R → R is not ‘onto’ function. Give reason.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×