SOLUTION: Find an equation for the inverse of y=2x^2-3. Identify the domain and range of each equation.

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Question 185447This question is from textbook saxon algebra 2
: Find an equation for the inverse of y=2x^2-3. Identify the domain and range of each equation.This question is from textbook saxon algebra 2

Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
There's a problem here: the equation y=2x%5E2-3 has no inverse over the domain . However, if we restrict the domain to be [), then we can find the inverse.


So...
Domain: [)
Range: [)


y=2x%5E2-3 Start with the given equation.


x=2y%5E2-3 Switch each "x" and "y". The goal is to now solve for "y"


x%2B3=2y%5E2 Add 3 to both sides.


%28x%2B3%29%2F2=y%5E2 Divide both sides by 2.


y%5E2=%28x%2B3%29%2F2 Rearrange the equation


y=sqrt%28%28x%2B3%29%2F2%29 Take the square root of both sides. Note: since we made the domain [), this means that we're only dealing with the positive square root.


So the inverse equation is y=sqrt%28%28x%2B3%29%2F2%29 where the domain and range is simply flipped:

Domain: [)
Range: [)