Grade 12Algebra

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

Manish Lohat

7 Years agoGrade 12

1 Answer

Susmita

7 Years ago

Write f(x)=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.

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

Manish Lohat

1 Answer

Susmita

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