मराठी

Find Gof And Fog When F : R → R And G : R → R Are Defined By F(X) = X And G(X) = |X| . - Mathematics

Advertisements
Advertisements

प्रश्न

Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x and g(x) = |x| .

Advertisements

उत्तर

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

 f(x) = x and g(x) = |x|

(gof) (x)

g ((x))

g (x)

|x|

fog) (x)

f (g (x))

f |x)

|x|

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

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 2 Functions
Exercise 2.2 | Q 1.4 | 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


Given examples of two functions fN → N and gN → N such that gof is onto but is not onto.

(Hint: Consider f(x) = x + 1 and `g(x) = {(x-1, ifx >1),(1, if x = 1):}`


Show that the logarithmic function  f : R0+ → R   given  by f (x)  loga x ,a> 0   is   a  bijection.


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.


Suppose f1 and f2 are non-zero one-one functions from R to R. Is `f_1 / f^2` necessarily one - one? Justify your answer. Here,`f_1/f_2 : R → R   is   given   by   (f_1/f_2) (x) = (f_1(x))/(f_2 (x))  for all  x in R .`


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


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x2 + 8 and g(x) = 3x3 + 1 .


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


If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?


Let f : [−1, ∞) → [−1, ∞) be given by f(x) = (x + 1)2 − 1, x ≥ −1. Show that f is invertible. Also, find the set S = {x : f(x) = f−1 (x)}.


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


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 : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]


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.


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

 

 


Let

\[f : R - \left\{ n \right\} \to R\]

\[f\left( x \right) = \frac{x - m}{x - n}, \text{where} \ m \neq n .\] Then,
 

\[f : R \to R\] is defined by

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

 


Which of the following functions from

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

 


Let  \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation

\[fog \left( x \right) = gof \left( x \right)\] is 



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

 


If  \[f\left( x \right) = \sin^2 x\] and the composite function   \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) 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),` how that f is one-one and onto. Hence, find f−1


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


Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.


Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

k = {(1,4), (2, 5)}


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

g(x) = |x|


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 → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.


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


The number of bijective functions from set A to itself when A contains 106 elements is ____________.


Which of the following functions from Z into Z is bijective?


Given a function If as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then


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: R → R be defined by f(x) = x2 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: N → N be defined by f(x) = x2 is ____________.

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


Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


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


Let f: R→R be a polynomial function satisfying f(x + y) = f(x) + f(y) + 3xy(x + y) –1 ∀ x, y ∈ R and f'(0) = 1, then `lim_(x→∞)(f(2x))/(f(x)` is equal to ______.


Which one of the following graphs is a function of x?

Graph A Graph B

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×