Pertanyaan

Diketahui dan .Nilai g( - 3) adalah ....

Diketahui $begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative sign 1 end exponent open parentheses 2 x close parentheses equals fraction numerator 3 over denominator 2 x minus sign 3 end fraction end style$ dan . Nilai g(-3) adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat sifat invers fungsi komposisi bahwa Sehingga, Kita cari terlebih dahulu. Maka Sehingga kita dapatkan Kemudian, kita cari g( x) . Jadi, . Dengan demikian, jawaban yang tepat adalah A.

Ingat sifat invers fungsi komposisi bahwa

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative sign 1 end exponent open parentheses 2 x close parentheses end cell equals cell fraction numerator 3 over denominator 2 x minus sign 3 end fraction end cell row cell open parentheses g to the power of negative sign 1 end exponent ring operator f to the power of negative sign 1 end exponent close parentheses open parentheses 2 x close parentheses end cell equals cell fraction numerator 3 over denominator 2 x minus sign 3 end fraction end cell end table end style$

Kita cari terlebih dahulu.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 1 over x plus 3 end cell row y equals cell 1 over x plus 3 end cell row cell y minus sign 3 end cell equals cell 1 over x end cell row cell x open parentheses y minus sign 3 close parentheses end cell equals 1 row x equals cell fraction numerator 1 over denominator y minus sign 3 end fraction end cell row cell f to the power of negative sign 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator x minus sign 3 end fraction end cell end table end style$

Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative sign 1 end exponent open parentheses 2 x close parentheses end cell equals cell fraction numerator 1 over denominator open parentheses 2 x close parentheses minus sign 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 x minus sign 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 x minus sign 3 end fraction end cell end table end style$

Sehingga kita dapatkan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g to the power of negative sign 1 end exponent ring operator f to the power of negative sign 1 end exponent close parentheses open parentheses 2 x close parentheses end cell equals cell fraction numerator 3 over denominator 2 x minus sign 3 end fraction end cell row cell g to the power of negative sign 1 end exponent open parentheses f to the power of negative sign 1 end exponent open parentheses 2 x close parentheses close parentheses end cell equals cell fraction numerator 3 over denominator 2 x minus sign 3 end fraction end cell row cell g to the power of negative sign 1 end exponent open parentheses fraction numerator 1 over denominator 2 x minus sign 3 end fraction close parentheses end cell equals cell fraction numerator 3 over denominator 2 x minus sign 3 end fraction end cell row cell g to the power of negative sign 1 end exponent open parentheses fraction numerator 1 over denominator 2 x minus sign 3 end fraction close parentheses end cell equals cell 3 open parentheses fraction numerator 1 over denominator 2 x minus sign 3 end fraction close parentheses end cell row cell g to the power of negative sign 1 end exponent open parentheses x close parentheses end cell equals cell 3 x end cell end table end style$

Kemudian, kita cari g(x).

Jadi, $begin mathsize 14px style g open parentheses negative sign 3 close parentheses equals fraction numerator negative sign 3 over denominator 3 end fraction equals minus sign 1 end style$ .

Dengan demikian, jawaban yang tepat adalah A.