Function notation/inverses

Function Notation

-(f+g)(x) ---> add equations

-(f-g)(x) ---> subtract equations

-(f closed circle g)(x) ---> multiply (only if closed circle)

-(f/g)(x) ---> divide

-(f open circle g)(x) or f(g(x))---> replace all x's in the f(x) equation with the equation g(x).

-If x is replaced w/ a number, plug into the equation. Ex: f(2); (f+g)(2); etc.

Example: x+2/ (x^2-4) = x+2/(x+2)(x-2)

The x+2's then cancel out, leaving you with 1/x-2

Inverses

To have an inverse that is a function it must pass the horizontal line test.

-To find the inverse you switch the x+y and solve for y.

-To prove something is an inverse do (f open circle f^-1)(x) and (f^-1 open circle f)(x). Both should simplify to x.

-f^-1(x) means inverse.

Example: Find the inverse of y= square root of x+3

x^2=square root of y+3^2

-square root ^2 cancels out

You're then left with x^2=y+3

-subtract 3 from each side.

Your answer is y=x^2-3 or f^-1(x)=x^2-3