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Question

Assuming a restricted domain in which the inverse is a function, find the inverse

f(x) = -6(x-2)^2

Answer 1

To solve this, switch the variables and solve for a new y-value.

In other words, replace your y-value (aka the f(x)) for an x, and switch your x-value for a y.

So it should look like this to start:

x = -6(y-2)²

Now the next step is to solve for y to be able to find the inverse.

So to start we have: x = -6(y-2)²,

Next we need to divide both sides by -6 to get: x/-6 = (y-2)²

Now, we need to square both sides of the equation and we have: (x/-6)^1/2 = y-2. (Raising the left hand side of the equation to 1/2 is another way to write a square root.)

Then, we add 2 to both sides of the equation to get the new y-value by itself and we have: (x/-6)^1/2 + 2 = y

So the inverse of our original equation is:

y' = (x/-6)^1/2 + 2

Answer 2

switch x and y, solve for y

x=-6(y-2)^2

take square roots

sqrx =sqr(-6)(y-2)

y-2 = sqrx/sqr(-6)

y = f^-1(x) = 2 + or - sqr(-x/6)