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How do you find the inverse of #f(x) =5/(x+1)#?

Answer 1

Christian Antunez

#f^(-1)(x)=5/x-1#

By definition, #y=f^(-1)(x) iff f(y)=x# #iff 5/(y+1)=x# #iff 5 = xy+x# #iff y=(5-x)/x=5/x-1#

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Answer 2

Christian Antunez

To find the inverse of a function ( f(x) ), you need to switch the roles of ( x ) and ( y ) and then solve for ( y ). Here's how you do it:

Start with the given function: ( f(x) = \frac{5}{x + 1} ).
Replace ( f(x) ) with ( y ): ( y = \frac{5}{x + 1} ).
Swap ( x ) and ( y ): ( x = \frac{5}{y + 1} ).
Solve for ( y ): [ x = \frac{5}{y + 1} ] [ x(y + 1) = 5 ] [ xy + x = 5 ] [ xy = 5 - x ] [ y = \frac{5 - x}{x} ]

So, the inverse of ( f(x) = \frac{5}{x + 1} ) is ( f^{-1}(x) = \frac{5 - x}{x} ).

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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.