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

The inverse is itself and yes, it is a function from

Given y, how do you find x?

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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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