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

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(35256) (Show Source): You can put this solution on YOUR website!
There's a problem here: the equation has no inverse over the domain

. However, if we restrict the domain to be [

), then we can find the inverse.

So...
Domain: [

)
Range: [

)

Start with the given equation.

Switch each "x" and "y". The goal is to now solve for "y"

Add 3 to both sides.

Divide both sides by 2.

Rearrange the equation

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 where the domain and range is simply flipped:

Domain: [

)
Range: [

)
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