Show that if f: R-{7/5}->R-{3/5} is d...

Show that if `f: R-{7/5}->R-{3/5}` is defined by `f(x)=(3x+4)/(5x-7)` and `g: R-{3/5}->R-{7/5}` is define by `g(x)=(7x+4)/(5x-3)` , then `fog=I_A` and `gof=I_B` , where `A=R-{3/5}, B=R-{7/5}; I_A(x)=x ,AAx in A , I_B(x)=x ,AAx in B` are called ide

`fog =I_(A) and gof=I_(A)`

`fog=I_(A) and gof=I_(B)`

`fog=I_(B) and gof=I_(B)`

`fog=I_(B) and gof I_(A)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

RELATIONS AND FUNCTIONS-2
DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos
RELATIONS AND FUNCTIONS-2
DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 2: Mappings, Mapping of Functions, Kinds of Mapping of Functions)|19 Videos
RELATIONS AND FUNCTIONS
DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos
SEQUENCES AND SERIES
DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

Show that if f:R-{(7)/(5)}rarr R-{(3)/(5)} is defined by f(x)=(3x+4)/(5x-7) and g:R-{(3)/(5)}rarr R-{(7)/(5)} is define by g(x)=(7x+4)/(5x-3), then fog=I_(A)A=R-{(3)/(5)},B=R-{(7)/(5)};I_(A)(x)=x,AA x in A,I_(B)(x)=x,AA x in B are called ideal

If f" R -{3/5} to R be defined by f(x)=(3x+2)/(5x-3) , then :

If f:R-{(7)/(5)}rarr R-{(3)/(5)} be defined as f(x)=(3x+4)/(5x-7) and g:R-{(3)/(5)}rarr R-{(7)/(5)} be defined as g(x)=(7x+4)/(5x-3). Show that gof=I_(A) and fog=I_(B), where B=R-{(3)/(5)} and A=R-{(7)/(5)}

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

Show that function f:A rarr B defined as f(x)=(3x+4)/(5x-7) where A=R-{7/5}, B=R-{3/5} is invertible and hence find f^(-1) .

Let f: R-{-3/5}->R be a function defined as f(x)=(2x)/(5x+3) . Write f^(-1) : Range of f->R-{-3/5} .

Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 and g(x)=3x-4

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

Let f : R rarr R be defined by f(x) = x^(2) + 3x + 1 and g : R rarr R is defined by g(x) = 2x - 3, Find, (i) fog (ii) gof

Find gof and gof when f: R->R and g: R->R is defined by f(x)=2x+3 and g(x)=x^2+5

DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)

If f: R to R, g: R to R and h: R to R is such that f(x)=x^(2), g(x)= t...
Text Solution
|
Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sin...
Text Solution
|
If f(x)=1+x+x^2+x^3+....oo for |x| < 1 then f^-1(x)=
Text Solution
|
Let f be a function with domain X and range Y. Let A, B sube X and C, ...
Text Solution
|
If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...
Text Solution
|
A binary operation * on the set {0,1,2,3,4,5} is defined as: a*b={...
Text Solution
|
Let * be a binary operation on N given by a*b=H C F\ (a ,\ b),\ \ a...
Text Solution
|
Show that the total number of binary operation from set A to A is n^(n...
Text Solution
|
If fQ to Q f(x)=2x,g,Q to Q, g (x)=x+2 then value of (fog)^(-1)(20) is
Text Solution
|
If g(x)=x-2 is the inverse of the function f(x)=x+2, then graph of g(x...
Text Solution
|
Which of the following is not a binary operation on the indicated set?
Text Solution
|
If f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2, ...
Text Solution
|
Let f(x)=(ax+b)/(cx+d). Then the fof (x) =x provided that
Text Solution
|
Let A={1,2,3,4,5} and functions f:A to and g: A to A to defined by f(1...
Text Solution
|
Suppose that f is an even function, g is an odd function and both f an...
Text Solution
|
If f(x)=e^(x) and g(x)= log(e)x, hen which of the following is true?
Text Solution
|
The inverse of the function f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2 is given ...
Text Solution
|
Show that if f: R-{7/5}->R-{3/5} is defined by f(x)=(3x+4)/(5x-7) a...
Text Solution
|
Let f:R to be defined by f(x)=3x^(2)-5 and g : R to R by g(x)=(x)/(x^...
Text Solution
|
Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then
Text Solution
|