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Q: You can use rational functions to study the relationships of inverse variation?

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A study of inverse relationships is one of a very large number of uses for rational functions. Only a rational function of a very special kind will be of any use.

yes

No. The additive inverse of zero or a negative rational number is not negative.

No, it is not. 3/5 is rational and its multiplicative inverse is 5/3 which is not an integer.

The inverse function of multiplication is division.

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A study of inverse relationships is one of a very large number of uses for rational functions. Only a rational function of a very special kind will be of any use.

yes

The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.

the output is halved

the output is divided by 3.

the output is divided by 4

The inverse variation is the indirect relationship between two variables. The form of the inverse variation is xy = k where k is any real constant.

If a variable X is in inverse variation with a variable Y, then it is in direct variation with the variable (1/Y).

If the multiplicative inverse exists then, by definition, the product is 1 which is rational.

Always, unless the original number is zero. This does not have an inverse.

The equation is xy = 22.5