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Diketahui fungsi f:x→f(x) didefinisikan oleh f(x)=x2 pada interval −1≤x≤3. b. Tentukan domain, kodomain, dan range!

Pertanyaan

Diketahui fungsi begin mathsize 14px style f colon x rightwards arrow f left parenthesis x right parenthesis end style didefinisikan oleh begin mathsize 14px style f open parentheses x close parentheses equals x squared end style pada interval begin mathsize 14px style negative 1 less or equal than x less or equal than 3 end style.

b. Tentukan domain, kodomain, dan range!

D. Noer

Master Teacher

Jawaban terverifikasi

Jawaban

 domain begin mathsize 14px style D subscript f equals open curly brackets x left enclose negative 1 less or equal than x less or equal than 3 semicolon x element of straight real numbers end enclose close curly brackets end style, kodomain begin mathsize 14px style K subscript f equals open curly brackets x left enclose x greater or equal than 0 semicolon x element of straight real numbers end enclose close curly brackets end style, dan range begin mathsize 14px style R subscript f equals open curly brackets x left enclose 0 less or equal than x less or equal than 9 semicolon x element of straight real numbers end enclose close curly brackets end style.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah domain begin mathsize 14px style D subscript f equals open curly brackets x left enclose negative 1 less or equal than x less or equal than 3 semicolon x element of straight real numbers end enclose close curly brackets end style, kodomain begin mathsize 14px style K subscript f equals open curly brackets x left enclose x greater or equal than 0 semicolon x element of straight real numbers end enclose close curly brackets end style, dan range begin mathsize 14px style R subscript f equals open curly brackets x left enclose 0 less or equal than x less or equal than 9 semicolon x element of straight real numbers end enclose close curly brackets end style.


- Domain (daerah asal)

begin mathsize 14px style D subscript f equals open curly brackets x left enclose negative 1 less or equal than x less or equal than 3 semicolon x element of straight real numbers end enclose close curly brackets end style 

- Kodomain (daerah kawan)

Untuk straight f left parenthesis straight x right parenthesis equals straight x squared space dan space straight x element of straight real numbers, kodomainnya adalah seluruh bilangan tak negatif atau seluruh bilangan positif dan 0.
Maka diperoleh 

begin mathsize 14px style K subscript f equals open curly brackets x left enclose x greater or equal than 0 semicolon x element of straight real numbers end enclose close curly brackets end style

- Range (daerah hasil)
untuk fungsi f left parenthesis x right parenthesis equals x squared dengan memasukkan nilai x pada interval negative 1 less or equal than x less or equal than 3, diperoleh

begin mathsize 14px style f left parenthesis negative 1 right parenthesis equals 1 end style
 begin mathsize 14px style f left parenthesis 0 right parenthesis equals 0 end style
begin mathsize 14px style f left parenthesis 3 right parenthesis equals 9 end style 

Maka diperoleh begin mathsize 14px style R subscript f equals open curly brackets x left enclose 0 less or equal than x less or equal than 9 semicolon x element of straight real numbers end enclose close curly brackets end style

 

Dengan demikian, domain begin mathsize 14px style D subscript f equals open curly brackets x left enclose negative 1 less or equal than x less or equal than 3 semicolon x element of straight real numbers end enclose close curly brackets end style, kodomain begin mathsize 14px style K subscript f equals open curly brackets x left enclose x greater or equal than 0 semicolon x element of straight real numbers end enclose close curly brackets end style, dan range begin mathsize 14px style R subscript f equals open curly brackets x left enclose 0 less or equal than x less or equal than 9 semicolon x element of straight real numbers end enclose close curly brackets end style.

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Diagram di atas menunjukkan pemetaan (fungsi) f dari himpunan P ke Q. Tentukan : a. daerah asal (domain),   b. daerah kawan (kodomain) c. daerah hasil (range)

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Jawaban terverifikasi

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