Question

What is the inverse of y=9x^2 -4

Answer 1

http://mathinsight.org/definition/inverse_function

Answer 2

First what you want to do replace every x with a y and replace every y with an x

so first you have y=9x^2-4
then you'll have
x=9y^2-4

now get y to be alone
to get y alone, first add 4 to both sides so you get
x+4 = 9y^2

now you can divide both sides by 9, so y can be alone
so you'll have
(x+4)/(9) = y^2

now to get rid of the square from the y, take the square root of both sides, so you'll have

sqrt(y^2) = sqrt((x+4)/(9))

the square root cancels out the power 2 in the y so you get

y = sqrt((x+4)/(9)) which can equal to y=sqrt((x+4))/(3) (since we did the square root of 9 is 3, you dont put a square root over the denominator anymore)