Find an equation of the inverse relation.
[tex]x=y^2-3y[/tex]
Choose the correct equation below.
A. [tex]y=3x-x^2[/tex]
B. [tex]y=x^2+3x[/tex]
C. [tex]xy^2=-3y[/tex]
D. [tex]y=x^2-3x[/tex]
Answer (1)
Swap x and y in the given equation: x = y 2 − 3 y becomes y = x 2 − 3 x .
The equation of the inverse relation is y = x 2 − 3 x .
Explanation
Swap x and y We are given the equation x = y 2 − 3 y and asked to find the equation of the inverse relation. To find the inverse, we swap x and y in the original equation.
Inverse Relation Swapping x and y in the equation x = y 2 − 3 y gives us y = x 2 − 3 x .
Final Answer Therefore, the equation of the inverse relation is y = x 2 − 3 x .
Examples
Consider a scenario where you want to convert temperatures from one scale to another, but the conversion involves a quadratic relationship. Finding the inverse relation allows you to easily convert back from the second scale to the original, streamlining the process and avoiding complex calculations each time. This is applicable in various scientific and engineering contexts where such conversions are necessary. For example, if x represents the temperature in Celsius and y represents a transformed temperature scale such that x = y 2 − 3 y , then the inverse relation y = x 2 − 3 x would allow you to convert back from the transformed scale to Celsius directly.
