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

Answer 1

Ariana Alvarez

The inverse is itself and yes, it is a function from #CC - {0}# to #CC#.

#f(x) = y Rightarrow x = f^(-1)(y)#

Given y, how do you find x?

Multiply by #x#.

#xy = 13#

Divide by #y#.

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

#13/text{thing} = f^(-1)(text{thing})#

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

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Answer 2

Elias Ackerman

To find the inverse of the function ( y = \frac{13}{x} ), we need to swap the roles of ( x ) and ( y ) and then solve for ( y ).

Start with the original equation: ( y = \frac{13}{x} ).
Swap ( x ) and ( y ): ( x = \frac{13}{y} ).
Solve for ( y ): Multiply both sides by ( y ) and divide both sides by ( x ).
The resulting equation will be the inverse function.

So, from ( x = \frac{13}{y} ), after solving for ( y ), we get: [ y = \frac{13}{x} ]

Therefore, the inverse function of ( y = \frac{13}{x} ) is itself: ( f^{-1}(x) = \frac{13}{x} ).

Now, to determine if it is a function, we need to check if it passes the vertical line test. Since ( f^{-1}(x) = \frac{13}{x} ) passes the vertical line test, it is a function.

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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.