Precalc0101to0102-page11 - (Section 1.1 Functions 1.1.10...

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(Section 1.1: Functions) 1.1.10 PART G: IMPLIED (OR NATURAL) DOMAIN Implied (or Natural) Domain If f is defined by: fx () = (an expression in x ), then the implied (or natural) domain of f is the set of all real numbers ( x values) at which the value of the expression is a real number. x could be replaced by another variable. Dom f is assumed to be the implied domain of f , unless otherwise specified or implied by the context. • In some applications (including geometry), we may restrict inputs to nonnegative and/or integer values (rounding may be possible). Implied Domain of an Algebraic Function If a function is algebraic, then its implied domain is the set of all real numbers except those that lead to (the equivalent of) …
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