हिंदी

Find Fog (2) and Gof (1) When : F : R → R ; F(X) = X2 + 8 and G : R → R; G(X) = 3x3 + 1. - Mathematics

Advertisements
Advertisements

प्रश्न

Find  fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → Rg(x) = 3x3 + 1.

उत्तर

(fog) (2f (g (2)(3×23+1f(25252 63

(gof) (1g (f (1)g (12+8g (93×93+2188

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 5 | पृष्ठ ४६

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Check the injectivity and surjectivity of the following function:

f: Z → Z given by f(x) = x2


Check the injectivity and surjectivity of the following function:

f: Z → Z given by f(x) = x3


Prove that the greatest integer function f: → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.


Show that the Signum Function f: R → R, given by `f(x) = {(1, if x > 0), (0, if x  = 0), (-1, if x < 0):}`  is neither one-one nor onto


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|)


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


Let A = {−1, 0, 1} and f = {(xx2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.


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 given by f(x) = x3


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


Verify associativity for the following three mappings : f : N → Z0 (the set of non-zero integers), g : Z0 → Q and h : Q → R given by f(x) = 2xg(x) = 1/x and h(x) = ex.


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 f −1 if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.


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 .`


If f : R → (−1, 1) defined by `f (x) = (10^x- 10^-x)/(10^x + 10 ^-x)` is invertible, find f−1.


If f : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.


Let A = {1, 2, 3, 4} and B = {ab} be two sets. Write the total number of onto functions from A to B.


A function f  from the set of natural numbers to integers defined by

`{([n-1]/2," when  n is  odd"   is ),(-n/2,when  n  is  even ) :}`

 

 


Let

\[f : R \to R\]
\[f\left( x \right) = \frac{x^2 - 8}{x^2 + 2}\]
Then,  f is


The function

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

Which of the following functions from

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

 


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

 


Let

\[f : [2, \infty ) \to X\] be defined by

\[f\left( x \right) = 4x - x^2\] Then, f is invertible if X =

 


Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R. Then, show that f is one-one.


Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(x, y): x is a person, y is the mother of x}


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


Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Raji wants to know the number of functions from A to B. How many number of functions are possible?

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Ravi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?

If `f : R -> R^+  U {0}` be defined by `f(x) = x^2, x ∈ R`. The mapping is


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


Let x is a real number such that are functions involved are well defined then the value of `lim_(t→0)[max{(sin^-1  x/3 + cos^-1  x/3)^2, min(x^2 + 4x + 7)}]((sin^-1t)/t)` where [.] is greatest integer function and all other brackets are usual brackets.


Let a and b are two positive integers such that b ≠ 1. Let g(a, b) = Number of lattice points inside the quadrilateral formed by lines x = 0, y = 0, x = b and y = a. f(a, b) = `[a/b] + [(2a)/b] + ... + [((b - 1)a)/b]`, then the value of `[(g(101, 37))/(f(101, 37))]` is ______.

(Note P(x, y) is lattice point if x, y ∈ I)

(where [.] denotes greatest integer function)


The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.


The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.


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 ______.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×