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Jika diketahui  dan , hasil dari  adalah ....

Jika diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator square root of 7 x plus 8 end root over denominator 2 x minus 5 end fraction end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 1 end style, hasil dari begin mathsize 14px style open parentheses f cross times g close parentheses left parenthesis 4 right parenthesis end style adalah ....

  1. 28space 

  2. 32space

  3. 34space

  4. 36space

  5. 42space

Jawaban:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator square root of 7 x plus 8 end root over denominator 2 x minus 5 end fraction end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 1 end style. Maka perkalian dua fungsi tersebut dapat dituliskan seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses f cross times g close parentheses left parenthesis x right parenthesis 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 cell open parentheses fraction numerator square root of 7 x plus 8 end root over denominator 2 x minus 5 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x squared plus 1 close parentheses end cell end table end style 

Hasil dari begin mathsize 14px style open parentheses f cross times g close parentheses left parenthesis 4 right parenthesis end style dapat dihitung dengan mensubstitusikan begin mathsize 14px style x equals 4 end style ke dalam fungsi begin mathsize 14px style open parentheses f cross times g close parentheses left parenthesis x right parenthesis end style seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f cross times g close parentheses left parenthesis 4 right parenthesis end cell equals cell open parentheses fraction numerator square root of 7 times 4 plus 8 end root over denominator 2 times 4 minus 5 end fraction close parentheses times open parentheses 4 squared plus 1 close parentheses end cell row blank equals cell open parentheses fraction numerator square root of 28 plus 8 end root over denominator 8 minus 5 end fraction close parentheses times open parentheses 16 plus 1 close parentheses end cell row blank equals cell open parentheses fraction numerator square root of 36 over denominator 3 end fraction close parentheses times open parentheses 17 close parentheses end cell row blank equals cell open parentheses 6 over 3 close parentheses times open parentheses 17 close parentheses end cell row blank equals 28 end table end style 

Dengan demikian, hasil dari begin mathsize 14px style open parentheses f cross times g close parentheses left parenthesis 4 right parenthesis end style adalah begin mathsize 14px style 28 end style.

Jadi, jawaban yang tepat adalah A.

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