PreCalc terms to know (And equations)

Function Operations (+, -, *, /)

(f + g)(x) = f(x) + g(x), same rule applies to other functions.

Function Operations (+, -, *, /), Domain

OVERLAPPING/COMMON Domain AND any natural restrictions (Radicand and denominators.)

Function composition

f(g(x)) or (f ∘ g)(x)

Plug g(x) into all x’s of f(x)

Function Composition Domain

(f ∘ g)(x) = f(g(x))

Input (g(x)) function’s domain AND any natural

restrictions (check radicals and fractions)

Decomposition

Find an inner and outer function that when composed

equals the given function

-this is the reverse/undoing of composition

One-to-One Function

Original AND inverse are both functions -original function passes Horizontal & Vertical Line tests

-no repeat x-values AND no repeat y-values

One-to-One Proof

Assume f(a) = f(b)

Show a = b

Inverse Functions Proof

Show BOTH f/g(x)0 = x AND g/f(x)0 = x

Domain & Range of Inverse Functions

Domain of f(x) = Range of f-1(x)

Range of f(x) = Domain of f-1(x)

--Domain of one function is Range of other

Inverse Domain Restrictions

Check that inverse function’s domain EQUALS the range of the original

AND/OR

Check that domain of original EQUALS the range of the inverse

Steps to find an Inverse

Switch x and y

Solve for y

Sketch original function (& inverse)

Check domain & range of original & inverse

Inverse Functions are Symmetric to...

The line y = x

Relation vs. Function

Functions must pass Vertical Line Test

Relations may or may not be a function—think ±√