Precalc0001to0005-page26

Precalc0001to0005-page26 - which will be discussed in...

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(Section 0.5: Exponents and Radicals: Laws and Forms) 0.5.4 PART D: FRACTIONAL, RADICAL, AND EXPONENTIAL FORMS Example Set 1 (Equivalent Expressions) The following tables list pairs of equivalent expressions, together with relevant restrictions. These restrictions are related to domains of functions, which will be discussed in Section 1.1. The restrictions guarantee that we never (do the equivalent of) … 1) divide by zero , or 2) take the even root of a negative value. WARNING 5 : Do not confuse exponential form with exponential functions,
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Unformatted text preview: which will be discussed in Chapter 3. Fractional Form Restrictions Exponential Form 1 x x ± x ± 1 1 x 2 x ± x ± 2 1 7 x ± 4/3 x ± 1 7 x 4/3 x ± ( ) (See Warnings below.) WARNING 6 : In the last example, we need to state the restriction x ± ( ) , because the expression 1 7 x ± 4/3 implies it, yet the expression 1 7 x 4/3 does not. WARNING 7 : It is incorrect to re-express 1 7 x ± 4/3 as 7 x 4/3 , a common error. Think of 1 7 x ± 4/3 as 1 7 ± 1 x ² 4/3 . The negative exponent only applies to x ....
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