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Jika diketahui dan . Hasil dari fungsi adalah ....

Jika diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus x minus 12 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x plus 6 end style. Hasil dari fungsi begin mathsize 14px style open parentheses g over f close parentheses left parenthesis x right parenthesis end style adalah ....

  1. begin mathsize 14px style fraction numerator 2 over denominator x minus 4 end fraction comma x not equal to 4 end style 

  2. begin mathsize 14px style fraction numerator 2 over denominator x plus 4 end fraction comma x not equal to negative 4 end style 

  3. begin mathsize 14px style fraction numerator 3 over denominator x minus 4 end fraction comma x not equal to 4 end style 

  4. begin mathsize 14px style fraction numerator 4 over denominator x minus 3 end fraction comma x not equal to 3 end style 

  5. begin mathsize 14px style fraction numerator 2 over denominator x minus 3 end fraction comma x not equal to 4 end style 

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g over f close parentheses left parenthesis x right parenthesis end cell equals cell fraction numerator g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator 2 x plus 6 over denominator x squared minus x minus 12 end fraction left parenthesis faktorkan space kedua space fungsi right parenthesis end cell row blank equals cell fraction numerator 2 up diagonal strike left parenthesis x plus 3 right parenthesis end strike over denominator left parenthesis x minus 4 right parenthesis up diagonal strike left parenthesis x plus 3 right parenthesis end strike end fraction end cell row blank equals cell fraction numerator 2 over denominator left parenthesis x minus 4 right parenthesis end fraction end cell end table end style
 

Hasil begin mathsize 14px style open parentheses g over f close parentheses left parenthesis x right parenthesis end style berupa pecahan, sehingga penyebut tidak boleh nol.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x minus 4 end cell not equal to 0 row straight x not equal to 4 end table end style
 

Oleh karena itu, jawaban yang benar adalah A.

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