Roboguru

Fungsi  dan  ditentukan oleh rumus  dan . Tentukan : Apakah  ? (Ya / Tidak)

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 :

Apakah begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight f close parentheses open parentheses straight x close parentheses equals straight x end style ? (Ya / Tidak)
 

 

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 terlebih dahulu 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row straight y equals cell 7 straight x minus 5 end cell row cell negative 7 straight x end cell equals cell negative 5 minus straight y end cell row straight x equals cell fraction numerator negative 5 minus straight y 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 5 minus straight x over denominator negative 7 end fraction end cell end table end style 
 

Kemudian kita analisis apakah benar  begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight f close parentheses open parentheses straight x close parentheses equals straight x end style


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 f close parentheses space open parentheses straight x close parentheses end cell equals cell fraction numerator negative 5 minus straight f open parentheses straight x close parentheses over denominator negative 7 end fraction end cell row blank equals cell fraction numerator negative 5 minus open parentheses 7 straight x minus 5 close parentheses over denominator negative 7 end fraction end cell row blank equals cell fraction numerator up diagonal strike negative 5 end strike minus 7 straight x plus up diagonal strike 5 over denominator negative 7 end fraction end cell row blank equals cell fraction numerator negative 7 straight x over denominator negative 7 end fraction end cell row blank equals straight x end table end style 
 

Jadi, benar bahwa   begin mathsize 14px style open parentheses straight f to the power of negative 1 end exponent ring operator straight f close parentheses open parentheses straight x close parentheses equals straight x end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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