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Perhatikan gambar berikut ini!

 

Gambar di atas merupakan diagram panah dari fungsi begin mathsize 14px style f colon P rightwards arrow Q end style dan size 14px g size 14px colon size 14px P size 14px rightwards arrow size 14px Q. Nilai dari size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis dan domain fungsi size 14px f size 14px times size 14px g secara berturut-turut adalah ...

  1. begin mathsize 14px style z squared end style dan begin mathsize 14px style open curly brackets 0 comma space 1 comma space 2 comma space 3 close curly brackets end style

  2. begin mathsize 14px style z squared end style dan begin mathsize 14px style open curly brackets 0 comma space 1 close curly brackets end style

  3. begin mathsize 14px style z squared end style dan begin mathsize 14px style open curly brackets 1 comma space 2 comma space 3 close curly brackets end style

  4. begin mathsize 14px style z end style dan undefined

  5. begin mathsize 14px style z end style dan begin mathsize 14px style open curly brackets 0 comma space 1 comma space 4 comma space 9 close curly brackets end style

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah B.space space space space  

Pembahasan

Ingat kembali bahwa size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px times size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis, sehingga diperoleh 

size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px times size 14px g size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px z size 14px times size 14px z size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px z to the power of size 14px 2 

Selanjutnya, untuk menentukan domain size 14px f size 14px times size 14px g, ingat kembali bahwa domain dari size 14px f size 14px times size 14px g adalah irisan dari domain fungsi begin mathsize 14px style f end style dan domain fungsi begin mathsize 14px style g end style, atau begin mathsize 14px style D subscript f times g end subscript equals D subscript f intersection D subscript g end style.

Dari soal, didapat size 14px D subscript size 14px f size 14px equals begin mathsize 14px style left curly bracket 0 comma 1 comma 2 comma 3 right curly bracket end style, dan size 14px D subscript size 14px g size 14px equals begin mathsize 14px style left curly bracket 0 comma 1 comma 4 comma 9 right curly bracket end style. Sehingga size 14px D subscript size 14px f size 14px times size 14px g end subscript size 14px equals size 14px D subscript size 14px f size 14px intersection size 14px D subscript size 14px g size 14px equals begin mathsize 14px style left curly bracket 0 comma space 1 right curly bracket end style.

Maka, nilai dari size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis dan domain fungsi size 14px f size 14px times size 14px g secara berturut-turut adalah begin mathsize 14px style z squared end style dan begin mathsize 14px style open curly brackets 0 comma space 1 close curly brackets end style.

Jadi, jawabannya adalah B.space space space space  

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Perhatikan gambar berikut ini!   Nilai dari (f ∙ g) (3)  dan domain fungsi (f ∙ g) (x)  adalah ....

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