मराठी

If F : R → R is Defined by F(X) = 3x + 2, Find F (F (X)). - Mathematics

Advertisements
Advertisements

प्रश्न

If f : R → R is defined by f(x) = 3x + 2, find f (f (x)).

उत्तर

f (f (x)) = f (3x +2)

= 3 (3x +2) +2

= 9x + 6 + 2

 = 9x + 8

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Functions - Exercise 2.5 [पृष्ठ ७४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 2 Functions
Exercise 2.5 | Q 35 | पृष्ठ ७४

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f: → N given by f(x) = x3


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


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.


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


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.


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|)


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 : R → R, defined by f(x) = sinx


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


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


Give examples of two surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective.


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.


Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.


Find fog and gof  if : f (x) = |x|, g (x) = sin x .


Let  f  be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.


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


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.


If f : Q → Qg : Q → Q are two functions defined by f(x) = 2 x and g(x) = x + 2, show that f and g are bijective maps. Verify that (gof)−1 = f−1 og −1.


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


If f : A → Ag : A → A are two bijections, then prove that fog is an injection ?


If f : A → Ag : A → A are two bijections, then prove that fog is a surjection ?


If A = {1, 2, 3} and B = {ab}, write the total number of functions from A to B.


Write the domain of the real function

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


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.


\[f : R \to R \text{given by} f\left( x \right) = x + \sqrt{x^2} \text{ is }\]

 

 


 \[f : A \to \text{B given by } 3^{ f\left( x \right)} + 2^{- x} = 4\] is a bijection, then

 

 

 

 


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,

 


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


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


The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.


The function f : R → R defined by f(x) = 3 – 4x is ____________.


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


A function f: x → y is said to be one – one (or injective) if:


Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are


If f: [0, 1]→[0, 1] is defined by f(x) = `(x + 1)/4` and `d/(dx) underbrace(((fofof......of)(x)))_("n"  "times")""|_(x = 1/2) = 1/"m"^"n"`, m ∈ N, then the value of 'm' 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 ______.


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)`.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×