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To find the inverse of the equation y = 2x2, we switch x and y to get x = 2y2 This presents the inverse relationship accurately. This equation represents the inverse relationship
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Therefore, the correct choice is d Thus, the correct option to simplify for finding the inverse is option d The equation that can be simplified to find the inverse of y = 2x2 is x = 2y2, which corresponds to option d
Interchanging x and y allows us to derive the inverse function effectively
Thus, the answer is option d. The problem asks us to identify the equation that represents the first step in finding the inverse of the function y=2x2 To find the inverse of a function, the standard procedure involves swapping the roles of the independent variable (usually x) and the dependent variable (usually y). Swapping x and y the given equation is y = 2x2
Swapping x and y, we get x = 2y2 Identifying the correct equation therefore, the equation that can be simplified to find the inverse of y = 2x2 is x = 2y2 Examples imagine you're converting temperatures between celsius and fahrenheit. To find the inverse of the equation y = 2x2, we need to manipulate the equation so that we can express y in terms of x
The process for finding the inverse function generally involves swapping x and y and then solving for y.
To find the inverse of y = 2x2, we rearrange it to get x = 2y2 as the simplified expression for the inverse The best choice from the options provided is d The equation x = 2y2 is now set up to find y in terms of x, which helps us in finding the inverse function The choice that corresponds to this process is x = 2y2.
An example of the inverse can be shown by taking specific values for x in the original equation, like x=1, which gives y=2(1)2=2 For the inverse, setting x=2 in x=2y2 allows us to find that y=1. The process of deriving the inverse function confirms the principles of algebra where we rearrange equations For quadratic functions like y = 2x2, taking the square root and isolating variables properly validates the comprehensive understanding of inverse relationships.
