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How do you find #f^-1(x)# given #f(x)=1/x#?

Answer 1

Ariana Alvarez

#f^-1 x= 1/x#

Let f(x) =y= #1/x#

Interchange x and y and solve for y. Accordingly it would be x=1/y, which would give y= #1/x#. So, it is #f^-1 x= 1/x#

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Answer 2

Elias Ackerman

To find the inverse function ( f^{-1}(x) ) given ( f(x) = \frac{1}{x} ), you swap the roles of ( x ) and ( y ) in the original function and solve for ( y ).

Start with the original function: ( f(x) = \frac{1}{x} ).
Swap ( x ) and ( y ): ( x = \frac{1}{y} ).
Solve for ( y ): ( x = \frac{1}{y} ) ( xy = 1 ) ( y = \frac{1}{x} ).

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