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Jika diketahui fungsi  dan . Daerah hasil dari  fungsi  untuk daerah asal  adalah ...

Pertanyaan

Jika diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals x squared minus 5 x plus 12 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x plus 8 end style. Daerah hasil dari  fungsi begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses end style untuk daerah asal begin mathsize 14px style open curly brackets x vertical line 0 less or equal than x less or equal than 8 comma space x space bilangan space real close curly brackets end style adalah ... 

  1. begin mathsize 14px style open curly brackets y vertical line 0 less or equal than y less or equal than 12 comma y space bilangan space real close curly brackets end style     

  2. begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than y less or equal than 8 comma y space bilangan space real close curly brackets end style 

  3. begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than y less or equal than 12 comma y space bilangan space real close curly brackets end style 

  4. begin mathsize 14px style open curly brackets y vertical line minus 8 less or equal than y less or equal than 4 comma y space bilangan space real close curly brackets end style       

  5. begin mathsize 14px style open curly brackets y vertical line minus 12 less or equal than y less or equal than 4 comma y space bilangan space real close curly brackets end style       

Pembahasan Soal:

Hasil dari fungsi begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses end style   adalah

begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses equals open parentheses x squared minus 5 x plus 12 close parentheses minus open parentheses 3 x plus 8 close parentheses space space space space space space space space space space space space space space equals x squared minus 8 x plus 4 end style

Daerah asal begin mathsize 14px style open curly brackets x vertical line 0 less or equal than x less or equal than 8 comma space x space bilangan space real close curly brackets end style

Daerah hasil dari fungsi begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses end style ditentukan dengan cara berikut

begin mathsize 14px style y equals x squared minus 8 x plus 4 end style

karena begin mathsize 14px style a greater than 0 end style maka grafik akan menghadap ke atas, dan akan dicari

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript m i n i m u m end subscript end cell equals cell fraction numerator b squared minus 4 a c over denominator negative 4 a end fraction end cell row blank equals cell fraction numerator open parentheses negative 8 close parentheses squared minus 8 open parentheses 1 close parentheses open parentheses 4 close parentheses over denominator negative 4 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 64 minus 32 over denominator negative 4 end fraction end cell row blank equals cell negative 12 end cell end table end style 

untuk begin mathsize 14px style x equals 0 end style maka begin mathsize 14px style y equals 0 squared minus 8 open parentheses 0 close parentheses plus 4 equals 4 end style 

untuk begin mathsize 14px style x equals 8 end style maka begin mathsize 14px style y equals 8 squared minus 8 open parentheses 8 close parentheses plus 4 equals 4 end style 

daerah hasil dari begin mathsize 14px style open parentheses f minus g close parentheses open parentheses x close parentheses equals x squared minus 8 x plus 4 end style adalah begin mathsize 14px style open curly brackets y vertical line minus 12 less or equal than y less or equal than 4 comma space y space bilangan space real close curly brackets end style

 Jadi, jawaban yang tepat  adalah E

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 11 April 2021

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