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How do you find the inverse of # y = -13/x# and is it a function?

Answer 1

Serenity Jones

See below.

To find the inverse we need to express #bbx# as a function of #bby#:

#y=-13/x#

#xy=-13#

#x=-13/y#

Substituting #x=y#

#f^-1(x)=-13/x#

This is an example of where a function is its own inverse.

We know that if we reflect the graph of a function in the line #bb(y=x)#, we will obtain its inverse. If you observe the graph of #bb(y=-13/x)#, after reflecting it in the line #bb(y=x)# it remains unchanged.

Hence it is its own inverse.

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Answer 2

Serenity Johnson

To find the inverse of ( y = -\frac{13}{x} ), swap the roles of ( x ) and ( y ) and solve for ( y ):

[ x = -\frac{13}{y} ]

[ xy = -13 ]

[ y = -\frac{13}{x} ]

The inverse of ( y = -\frac{13}{x} ) is itself, ( y = -\frac{13}{x} ).

This function is not defined for ( x = 0 ). Therefore, it is not a function because for some values of ( x ), there are multiple corresponding values of ( y ). Specifically, for any nonzero value of ( x ), there are two corresponding values of ( y ).

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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.