To find the inverse of the equation y = 5x² + 10, we need to follow a few steps to rearrange the equation in terms of x.
First, replace y with x:
x = 5y² + 10
Next, isolate the term with y:
x – 10 = 5y²
Now, divide both sides by 5:
(x – 10) / 5 = y²
To solve for y, take the square root of both sides:
y = ±√((x – 10) / 5)
Since we usually consider only the positive branch for the inverse of a quadratic function, we can simplify this to:
y = √((x – 10) / 5)
This is the simplified equation that gives us the inverse function of the original equation.