Roboguru

Fungsi  dan  ditentukan oleh rumus  dan . Tentukan :

Pertanyaan

Fungsi begin mathsize 14px style straight f space colon space straight R rightwards arrow straight R end style dan begin mathsize 14px style straight g space colon space straight R rightwards arrow straight R end style ditentukan oleh rumus begin mathsize 14px style straight f open parentheses straight x close parentheses equals 7 straight x minus 5 end style dan begin mathsize 14px style straight g open parentheses straight x close parentheses equals 4 straight x plus 9 end style. Tentukan :
 

begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent close parentheses open parentheses straight x close parentheses end style  

Pembahasan Soal:

Pertama kita tentukan invers dari begin mathsize 14px style straight f open parentheses straight x close parentheses equals 7 straight x minus 5 end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell 7 straight x minus 5 end cell row straight y equals cell 7 straight x minus 5 end cell row cell negative 7 straight x end cell equals cell negative straight y minus 5 end cell row straight x equals cell fraction numerator negative straight y minus 5 over denominator negative 7 end fraction end cell row sehingga colon blank row cell straight f to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative straight x minus 5 over denominator negative 7 end fraction end cell end table end style 
 

Selanjutnya kita tentukan invers dari  begin mathsize 14px style straight g open parentheses straight x close parentheses equals 4 straight x plus 9 end style
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight g open parentheses straight x close parentheses end cell equals cell 4 straight x plus 9 end cell row straight y equals cell 4 straight x plus 9 end cell row cell negative 4 straight x end cell equals cell negative straight y plus 9 end cell row straight x equals cell fraction numerator negative straight y plus 9 over denominator negative 4 end fraction end cell row sehingga colon blank row cell straight g to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative straight x plus 9 over denominator negative 4 end fraction end cell end table end style 
 

Maka begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent close parentheses open parentheses straight x close parentheses end style  sebagai berikut :
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent close parentheses open parentheses straight x close parentheses end cell equals cell fraction numerator negative open parentheses straight g to the power of negative 1 end exponent open parentheses straight x close parentheses close parentheses minus 5 over denominator negative 7 end fraction end cell row blank equals cell fraction numerator negative open parentheses begin display style fraction numerator negative straight x plus 9 over denominator negative 4 end fraction end style close parentheses minus 5 over denominator negative 7 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator straight x minus 9 over denominator negative 4 end fraction end style minus open parentheses begin display style fraction numerator negative 20 over denominator negative 4 end fraction end style close parentheses over denominator negative 7 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator straight x minus 9 plus 20 over denominator negative 4 end fraction end style over denominator negative 7 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator straight x plus 11 over denominator negative 4 end fraction end style over denominator negative 7 end fraction end cell row blank equals cell fraction numerator negative 7 open parentheses straight x plus 11 close parentheses over denominator negative 4 end fraction end cell row blank equals cell fraction numerator negative 7 straight x minus 77 over denominator negative 4 end fraction end cell end table end style 
 

Jadi, begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent close parentheses open parentheses straight x close parentheses equals fraction numerator negative 7 straight x minus 77 over denominator negative 4 end fraction end style 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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