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How do you find the inverse of #f(x)=x/(x+1)#?

Answer 1

Chloe Alexander

#y=-x/(x-1)#

Change to #y=x/(x+1)#.

Swap the #x# and #y#.

#x=y/(y+1)#

Solve for #y#.

#x(y+1)=y# #xy+x=y# #xy-y=-x# #y(x-1)=-x# #y=-x/(x-1)#

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Answer 2

Ariana Alvarez

To find the inverse of ( f(x) = \frac{x}{x+1} ), follow these steps:

Replace ( f(x) ) with ( y ).
Swap ( x ) and ( y ).
Solve the equation for ( y ).
Replace ( y ) with ( f^{-1}(x) ).

Step 1: ( y = \frac{x}{x+1} )

Step 2: Swap ( x ) and ( y ): ( x = \frac{y}{y+1} )

Step 3: Solve for ( y ): [ x(y + 1) = y ] [ xy + x = y ] [ xy - y = -x ] [ y(x - 1) = -x ] [ y = \frac{-x}{x - 1} ]

Step 4: Replace ( y ) with ( f^{-1}(x) ): [ f^{-1}(x) = \frac{-x}{x - 1} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.