MAT 101 Lecture Notes - Square Root, Even And Odd Functions, Inverse Function
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Example 2. 1 find the domains and ranges of the following functions. (cid:1858):(cid:1850) (cid:1851) (cid:1876) (cid:1850) (cid:1877) (cid:1851) (cid:1871)(cid:1873)(cid:1855) (cid:1872) (cid:1853)(cid:1872) (cid:1877)=(cid:1858)((cid:1876)). A function (cid:1858) from a set (cid:1850) to a set (cid:1851) is a rule that assigns a unique (single) element. ((cid:1876)) (cid:1851) to each element (cid:1876) (cid:1850), i. e. the set (cid:1850) of all possible input values is called the domain (cid:1830)(cid:3033) of the function (cid:1830)(cid:3033)={(cid:1876) :(cid:1877)=(cid:1858)((cid:1876))}. The set of all values of (cid:1858)((cid:1876)) as (cid:1876) varies throughout (cid:1830)(cid:3033) is called the range of the (cid:1844)(cid:3033)=(cid:3419)(cid:1877) (cid:1851):(cid:1877)=(cid:1858)((cid:1876)) (cid:1876) (cid:1830)(cid:3033) (cid:3423). The range may not include every element in the set (cid:1851). (cid:1854)) (cid:1877)=1(cid:1876) (cid:1853)) (cid:1877)=(cid:1876)(cid:2870) (cid:1855)) (cid:1877)= (cid:1876) (cid:1856)) (cid:1877)= 4 (cid:1876) (cid:1857)) (cid:1877)=(cid:3493)1 (cid:1876)(cid:2870: the formula (cid:1877)=(cid:1876)(cid:2870) has been defined for all real number (cid:1876) , so (cid:1830)(cid:3033)= =( , ). The range of (cid:1877)=(cid:1876)(cid:2870) is (cid:1844)(cid:3033)=[0, ) number y is the square of its own square root, (cid:1877)=(cid:3435)(cid:3493)(cid:1877)(cid:3439)(cid:2870) for (cid:1877) 0.
