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Diketahui  dan . Nilai dari  adalah ...

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals 2 x squared minus 3 x plus 4 dan g left parenthesis x right parenthesis equals 4 x minus 5. Nilai dari open parentheses g ring operator f close parentheses open parentheses 2 close parentheses adalah ...

Pembahasan Soal:

Komposisi dari dua fungsi open parentheses g ring operator f close parentheses open parentheses x close parentheses adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses 2 x squared minus 3 x plus 4 close parentheses end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 4 open parentheses 2 x squared minus 3 x plus 4 close parentheses minus 5 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 8 x squared minus 12 x plus 16 minus 5 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 8 x squared minus 12 x plus 11. end cell end table

Selanjutnya, nilai dari open parentheses g ring operator f close parentheses open parentheses 2 close parentheses adalah menyubstitusikan x equals 2 ke fungsi komposisi open parentheses g ring operator f close parentheses open parentheses x close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 close parentheses squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 12 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 11 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 32 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 24 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 11 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 19 end table

Dengan demikian, nilai dari open parentheses g ring operator f close parentheses open parentheses 2 close parentheses adalah 19.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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