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**Precalculus10**

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NON REVERSIBLE-if/then -conditional ture -converse false

Lesson 3.4 The Logic of Equation Solving

3. If h is 1.1, then for all x in the domains of f and g for which f(x) and g(x) are in the domain of h: f(x)=g(x) <=>h(f(x))=h(g(x))(Function Composition Property of Equality)

Reversible Steps Theorem:Let f, g, and h be functios. Then, for all x in the intersection of the domains of functions f, g, and h...

1. f(x)=g(x) <=>f(x)+h(x)=g(x)+h(x)(Addition Property of Equality)

2. f(x)=g(x) <=>f(x)*h(x)=g(x)*h(x)(Multiplication Property of Equality)

Zero-Product Property:(ab=0)=> (a=0 or b=0)

REMEMBER TO CHECK YOUR RESULTS ON EQUATIONS !

x=1 multiply by x on both sides x^2=x solutions=0 and 1CAREFUL IN MULTIPLYING BOTH SIDES BY A VALUE!(Do not multiply by 0!)

CAREFUL IN LOOSING OR GAINING VALUES AFTER SOLVING EQUATIONS!

REVERSIBLE-If and only if -equivalent equations -converse true

ex :1.1 functions, x^3, +, -, x and /

ex: x^2, multiplication by 0

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