find ( f^{-1} ) for the one - to - one function ( f ).\n( f(x)=\frac{1}{x} )\n( f^{-1}(x)= )
find ( f^{-1} ) for the one - to - one function ( f ).\n( f(x)=\frac{1}{x} )\n( f^{-1}(x)= )
Answer
Explanation:
Step1: Set ( y = f(x) )
Given ( f(x)=\frac{1}{x} ), so ( y = \frac{1}{x} ).
Step2: Swap ( x ) and ( y )
After swapping, we get ( x=\frac{1}{y} ).
Step3: Solve for ( y )
Multiply both sides by ( y ): ( xy = 1 ). Then ( y=\frac{1}{x} ).
Answer:
( f^{-1}(x)=\frac{1}{x} )