# LOS JACKIES

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Function Laws

LOS JACKIES

3.2Definition f gSuppose that f and g are functions. The composite of f with g , written f g, is the function with rule f g(x)= f(g(x))Whose domain in the set of all x in the domain of f for which f(x) is in the domain of g. Example:f(x)= x+3g(x)= 5x-2 f g(x)= 5x+1Domain= real numbers

3.1Definitions of Basic arithmetic operations on functions:Suppose f and g are real valued functions define don a set S of real numbers, were S is the intersection of the domain f and domain of g. Then f+g , f-g, f * g, f/g are the functions defined such that for all x in S: (f+g)(x)= f(x) + g(x)(f-g)(x)= f(x) – g(x)(f * g)(x)=f(x) * g(x)(f/g)(x)=f(x)/g(x), provided g(x) 0Example:If f(x) = 5x +2 g(x)=6x+3Then, (f+g)= (5x +2)+(6x+3) =11x+5

3.4Addition Property of Equality:For all real numbers a, b, and c:a=b a+c=b+cExample:4x -2 = 324+ (4x-2) = (32) +4Multiplication Property of Equality:For all real numbers a and b, and for c0:a=b ac=bcExample:4x -2 = 324(4x-2) = (32)4

3.3Definition of inverse functionf and g are inverse functions, written f = g -1 or g= f -1, if and only if f g(x)=x for all x in the domain of g and g f(x)=x for all x in the domain of f. Example:Log 2 (x) = 2 xDefinition of one to one FunctionFor every y there is only one x AND for every x there is only one y.Example:y=xFunction Inverse TheoremA function has an inverse that is a function if and only if it is a 1-1 functionExample:y(x)=x y-1(x)=x

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