Question

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

Answer 1

3x^2=y-4, x^2=(y-4)/3 and x=sqrt((y-4)/3) where the positive and negative square roots are implied. This is still a function, because when it is graphed, it is identical to the original function (parabola). However, if the positive square root only is implied, only half the parabola is implied, and its reflection in the axis of symmetry would be missing.

Answer 2

Given y = 3x^2+4

To solve for the inverse you switch the x and y in the equation and then solve in terms of y.

x = 3y^2+4

x - 3y^2 = 4

-3y^2 = 4 - x

3y^2 = x - 4

y^2 = (x-4)/3

y = √((x-4)/3)

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