Question

Find the inverse of y=3x^2+4.  Is the inverse a function?

Answer 1

Given y = 3x^2+4

Interchange x and y .

x = 3y^2+4

Subtract x from each side.

3y^2+(4-x) = 0

To find inverse solve for y.

Compare it to quadratic equaton ax^2+bx+c = 0

 

Comments

y = ± [√12√(x - 4)] / (2 * 3)

y = ± [2√3√(x - 4)] / (2 * 3)

y = ± [√3√(x - 4)] / 3

y = ± √(x - 4) / √3.

Therefore, inverse of the given function ± √(x - 4) / √3.