If f(y)=(y)/(sqrt(1-y^(2))),g(y)=(y)/(sq...

If `f(y)=(y)/(sqrt(1-y^(2))),g(y)=(y)/(sqrt(1+y^(2)))` then show that `("fog")(y)=y`

Answer

Step by step text solution for If f(y)=(y)/(sqrt(1-y^(2))),g(y)=(y)/(sqrt(1+y^(2))) then show that ("fog")(y)=y by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

FUNCTIONS
SRISIRI PUBLICATION|Exercise EXERCISE(MISCELLANEOUS)|27 Videos
FUNCTIONS
SRISIRI PUBLICATION|Exercise EXERCISE(DOMAINS AND RANGES)|40 Videos
DIFFERENTIATION
SRISIRI PUBLICATION|Exercise EXERCISE(VSAQ,SAQ & LAQ)|14 Videos
HYPERBOLIC FUNCTIONS
SRISIRI PUBLICATION|Exercise SPQ|8 Videos

Similar Questions

Explore conceptually related problems

If f(y) = y/(sqrt1-y^2), g(y) = y/(sqrt(1+y^2)) then show that fog(y) = y .

y = sqrt(1 + x^(2)) : y' = (xy)/(1 + x^(2))

Knowledge Check

If e^(x) = y + sqrt(1+y^2) then y =

A

`(e^(x) +e^(-x))/2`

B

`(e^(x)-e^(-x))/2`

C

`e^(x)+e^(-x)`

D

`e^(x)-e^(-x)`

If sqrt(1- x ^(2)) + sqrt(1- y ^(2) ) = a (x -y) then (dy)/(dx)=

A

`(sqrt(1 + y ^(2)))/( sqrt(1+ x ^(2)))`

B

`(sqrt(1 + x ^(2)))/( sqrt(1+ y ^(2)))`

C

`(sqrt(1 - y ^(2)))/( sqrt(1+ x^(2)))`

D

`(sqrt(1 - y ^(2)))/( sqrt(1- x^(2)))`

If sqrt(1+ x ^(2)) + sqrt(1 + y ^(2)) =a ( x -y) then (dy)/(dx) =

A

`(sqrt(1 + y 2))/(sqrt(1+ x ^(2)))`

B

`(sqrt(1 + x 2))/(sqrt(1+ y ^(2)))`

C

0

D

1

Similar Questions

Explore conceptually related problems

If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)

If y=f(x)=(2x-1)/(x-2), then f(y)=

If sqrt( 1 - x^2) + sqrt( 1 - y^2) = a ( x -y) , then show that (dy)/(dx) = sqrt( 1-y^2)/( 1-x^2) .

If sqrt(1 - x^(2)) + sqrt(1 - y^(2)) = a(x - y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2))) .

If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

SRISIRI PUBLICATION-FUNCTIONS-EXERCISE(VSAQ)

If f(y)=(y)/(sqrt(1-y^(2))),g(y)=(y)/(sqrt(1+y^(2))) then show that ("...
02:57
|
If f:RtoR,g:RtoR are defined by f(x)=2x^(2)+3 and g(x)=3x-2, then find...
02:32
|
If f:RtoR,g:RtoR are defined by f(x)=2x^(2)+3 and g(x)=3x-2, then find...
02:03
|
If f:RtoR,g:RtoR are defined by f(x)=2x^(2)+3 and g(x)=3x-2, then find...
02:06
|
If f:RtoR,g:RtoR are defined by f(x)=2x^(2)+3 and g(x)=3x-2, then find...
03:11
|
f:R-{0} to R is defined as f(x)=x+1/x then show that (f(x))^(2)=f(x^(2...
01:59
|
If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3), then S.T f(x) +...
01:39
|
If f:R-(pm1)toR is defined by f(x)=log|(1+x)/(1-x)|, then show that f(...
03:37
|
If f:R to R,g:R to R are defined by f(x)=3x-2,g(x)=x^(2)+1, then find ...
02:54
|
If f:R to R,g:R to R are defined by f(x)=3x-2,g(x)=x^(2)+1, then find ...
02:21
|
If f:R to R,g:R to R are defined by f(x)=2x-3,g(x)=x^(3)+5 then find (...
02:58
|
If f(x)=1+x+x^(2)+..... for |x|lt1 then show that f^(-1)(x)=(x-1)/(x)
00:44
|
If f(x)=(x-1)/(x+1),x ne pm1, show that fof^(-1)(x)=x.
04:29
|
If f:[1,oo) to [1,oo) is defined by f(x) = 2^(x(x-1)) then find f^(-1)...
03:42
|
If f(x)=e^(x) and g(x)=log(e)x, then show that "fog=gof" and find f^(-...
03:30
|
Let f(x) = x^(2), g(x) = 2^(x). Then solve the equation (fog)(x)=(gof)...
01:27
|
On what domain the functions f(x)=x^(2)-2x and g(x)=-x+6 are equal?
02:35
|
If f(x) = (cos^(2)x+sin^(4)x)/(sin^(2)x + cos^(4)x) AA x in R then sho...
02:23
|
If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(t...
02:05
|
Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,34,}. to B={1...
03:02
|