मराठी

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

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

Advertisements

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Functions - Exercise 2.2 [पृष्ठ ४६]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 2 Functions
Exercise 2.2 | Q 1.2 | पृष्ठ ४६

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f : R → R given by f(x) = x2


Give examples of two functions fN → Z and gZ → Z such that g o f is injective but gis not injective.

(Hint: Consider f(x) = x and g(x) =|x|)


Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)


Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x2


Classify the following function as injection, surjection or bijection :

f : Z → Z, defined by f(x) = x2 + x


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = sinx


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


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


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


Give examples of two one-one functions f1 and f2 from R to R, such that f1 + f2 : R → R. defined by (f1 + f2) (x) = f1 (x) + f2 (x) is not one-one.


Let f : N → N be defined by

`f(n) = { (n+ 1, if n  is  odd),( n-1 , if n  is  even):}`

Show that f is a bijection. 

                      [CBSE 2012, NCERT]


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


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

.


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


Which one of the following graphs represents a function?


If f : R → R is defined by f(x) = x2, write f−1 (25)


If f : R → R is given by f(x) = x3, write f−1 (1).


If f : R → Rg : R → are given by f(x) = (x + 1)2 and g(x) = x2 + 1, then write the value of fog (−3).


What is the range of the function

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


Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)}                                                                                                        [NCERT EXEMPLAR]


The range of the function

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

 


Which of the following functions from

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

to itself are bijections?

 

 

 


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

\[f : R \to R, f\left( x \right) = x^2\]
 

If \[g \left( f \left( x \right) \right) = \left| \sin x \right| \text{and} f \left( g \left( x \right) \right) = \left( \sin \sqrt{x} \right)^2 , \text{then}\]

 


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


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

 


Show that the function f: R → R defined by f(x) = `x/(x^2 + 1)`, ∀ ∈ + R , is neither one-one nor onto


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


The function f : R → R given by f(x) = x3 – 1 is ____________.


Let f: R → R defined by f(x) = x4. Choose the correct answer


Let f: R → R defined by f(x) = 3x. Choose the correct answer


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


If f; R → R f(x) = 10x + 3 then f–1(x) is:


Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.


Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals ______.


A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×