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

Answer 1

Sophie Adams

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

#f(x) = 1/x=># write #x# as a function of #y:#

#y = 1/x=># switch #x and y:#

#x = 1/y=># solve for #y:#

#y=1/x=># this is the inverse function of #f(x):# hence

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

To check let#:f(x)=1/x , g(x)=1/x:#

#g(f(x)) = 1/(1/x) = x# and#f(g(x))=1/(1/x)=x:#

hence #g# is the inverse of #f# and #f# is the inverse of #g.#

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Answer 2

Benjamin Achtenberg

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

Replace ( f(x) ) with ( y ).
Swap ( x ) and ( y ) to obtain the equation in terms of ( y ).
Solve the resulting equation for ( y ).
Replace ( y ) with ( f^{-1}(x) ) to express the inverse function.

Starting with ( y = \frac{1}{x} ), swap ( x ) and ( y ) to get ( x = \frac{1}{y} ). Then solve for ( y ) to find the inverse function.

( x = \frac{1}{y} )
( xy = 1 )
( y = \frac{1}{x} )

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