السلام عليكم.

the function,f and g,given by : f(x)=x^2-4x+4,and g(x)=2sin(x).;l
a)find the domian of the functionh(x)=g(x)\f(x),l
b)show that f is not one-one,and determine(the largest) sub-domians on which f is one-one.find the inverse of f on a sub-domian containing,the value, x=2
c)find the function g(f(x)) and specify the range and the domian of this function.

شكرا جميعا لو سمحتوا افيدوني قريبا.

 

 

السلام عليكم.

the function,f and g,given by : f(x)=x^2-4x+4,and g(x)=2sin(x).;l
a)find the domian of the functionh(x)=g(x)\f(x),l
b)show that f is not one-one,and determine(the largest) sub-domians on which f is one-one.find the inverse of f on a sub-domian containing,the value, x=2
c)find the function g(f(x)) and specify the range and the domian of this function

ولو سمحتوا اعينوني لأن لدي امتحان غدا فيه.....

 

 

.{2}/a)domainR
b)is one to one andf invers=x^1/2-2
g(f(x)) =2Sin(x^2-4x+4)and domain is R and rangeis [-1,1]that is all

 

 

عفوا يا اخي شكرا لحلك ولكن كيف طريقة الحل ...؟؟؟؟

شكرا

 

 

1- f(x) = ( x-2 ) ^2
2- h ( x ) = g /f ...... domain h ( x) all x not x= 2
3- g( f( x) =2 sin ( x- 2 ) ^ 2