# Los preguerreros

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**Precalculus10**

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LESSON 3.3

Definition of inverse function:F and g are inverse functions if and only if f composed g(x)=x for x in the domain of g and g composed f(x)=x for all x in the domain of f.

One-to-one function inverse theorem:Every value of Y has a value of X and every value of X has a value of Y.

NOT A ONE TO ONE FUNCTION

Definition Arithmetic Operations:1) (f+g)(x)= f(x) + g(x)2) (f-g)(x)= f(x) - g(x)3) (f*g)(x)= f(x) * g(x)4) (f/g)(x)= f(x) / g(x)

Lesson 3.1

Arithmetic Operations of Sequences:For sequences U and V, for all integers n for which both sequences are defined1) (U+V)n= Un + Vn2) (U-V)n= Un - Vn3) (U*V)n= Un * Vn4) (U/V)n= Un / Vn

Definition of g°f: The composite of g and f is written with the rule:g°f(x)= g(f(x))Domain: the set of all x in the domain of f for which f(x) is in the domain of g. x must be in the domain of f for f(x) to be defined, and f(x) must be in the domain of g for g(fx)) to be defined.

Lesson 3.2

Decomposition: The process of finding a single function as a composite of two or more functions.

Lesson 3.4

When solving an equation there are some operations more complicated than adding or multiplying both sides, like squaring both sides and taking the log of both sides. In these operations you can gain or lose solutions.

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