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Diketahui fungsi . Jika daerah asal  adalah , daerah hasil fungsi  adalah ...

Pertanyaan

Diketahui fungsi f colon x rightwards arrow 3 minus x squared. Jika daerah asal f adalah D subscript f equals open curly brackets x vertical line minus 4 less than x less or equal than 3 comma x element of R close curly brackets, daerah hasil fungsi y equals open vertical bar f open parentheses x close parentheses close vertical bar adalah ...

  1. open curly brackets x vertical line 0 less or equal than y less or equal than 13 comma x element of R close curly brackets 

  2. open curly brackets x vertical line 0 less or equal than y less than 13 comma x element of R close curly brackets  

  3. open curly brackets x vertical line 0 less than y less or equal than 13 comma x element of R close curly brackets  

  4. open curly brackets x vertical line 3 less than y less than 13 comma x element of R close curly brackets  

  5. open curly brackets x vertical line 3 less or equal than y less than 13 comma x element of R close curly brackets  

Pembahasan Soal:

Diketahui dari soal 

f open parentheses x close parentheses equals 3 minus x squared D subscript f equals open curly brackets x vertical line minus 4 less than x less or equal than 3 comma x element of R close curly brackets 

Daerah asal 

open curly brackets negative 3 comma negative 2 comma negative 1 comma 0 comma 1 comma 2 comma 3 comma close curly brackets

maka range dari y equals open vertical bar f open parentheses x close parentheses close vertical bar sebagai berikut

y equals open vertical bar 3 minus open parentheses negative 3 close parentheses squared close vertical bar equals open vertical bar 3 minus 9 close vertical bar equals 6 y equals open vertical bar 3 minus open parentheses negative 2 close parentheses squared close vertical bar equals open vertical bar 3 minus 4 close vertical bar equals 5 y equals open vertical bar 3 minus open parentheses negative 1 close parentheses squared close vertical bar equals open vertical bar 3 minus 1 close vertical bar equals 2 y equals open vertical bar 3 minus 0 squared close vertical bar equals 3 y equals open vertical bar 3 minus 1 squared close vertical bar equals 2 y equals open vertical bar 3 minus 2 squared close vertical bar equals 1 y equals open vertical bar 3 minus 3 squared close vertical bar equals 6 

sehingga daerah hasilnya R subscript f equals open curly brackets x vertical line 0 less or equal than y less than 13 comma x element of R close curly brackets 

Jadi, jawaban yang tepat adalah C

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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