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Grade: 12

                        

If,we have the following function F(x) =(2 x -2 -x ) /(2 x +2 -x ) Find f -1 (x).

2 years ago

Answers : (1)

Susmita
425 Points
							
Write f(x)=y.
So 
y=
f(x)=\frac{2^x -\frac{1}{2^x}}{2^x+\frac{1}{2^x}}
=\frac{4^x -1}{4^x+1}
Swap x and y.
Or,x=\frac{4^y -1}{4^y +1}
Or,\frac{x+1}{x-1} =\frac{(4^y -1)+(4^y+1)}{(4^y-1)-(4^y +1)}
Or,\frac{x+1}{x-1} =\frac{(2*4^y)}{(-2)}
Or,\frac{x+1}{x-1} =-4^y
Take logarith on both side.
Or,\log \frac{x+1}{x-1} =-y\log 4
Find y and write y=f-1(x).
Or,y=\log ( \frac{x-1}{x+1} -4)=f^-1(x)
Hope this helps.
2 years ago
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