This is my senior year, and for math I’m taking AP Calculus AB. It’s a challenging course, especially when almost everyday we learn a new lesson. So I must admit I don’t always understand what we’re learning, but one I did understood was My Inverse Function.
Let’s start by stating that f(x) is the same as ‘y’
They give you an equation and a y-value…
For example: f(x)=X^2 (it means X-squared) and f(6)=36; the number in the parenthesis is the X-value, and the 36 is the y-value.
The next step is to make the first function inverse.. So since f(x) is originally y, it becomes X, and the y-value in the function becomes x… So f(x)=X^2 becomes X=y^2.
After inverting them, you have to find the derivative… Variables always have the value of 1, since it’s thought that their exponent is of one. And the variables that do have exponents, the number is brought to the front of the variable and the new exponent is -1 of the original number… So x=y^2 becomes 1=2y dy/dx
Then the number after the equal sign becomes the denominator of the number before the equal sign (1/2y) and the dy/dx stay on the other side of the equal sign… So now it looks like this 1/2y=dy/dx
After that, dy/dx is canceled. And using the equation, we plug in the X-value, which originally was 6 (remember f(6)=36) …And now we have 1/2(6) which equals to 1/12…and thats your final answer.