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Diketahui  dan . b. Apakah. c. Sifat apakah yang dapat kalian temukan dari fungsi invers pada fungsi komposisi !

Pertanyaan

Diketahui f open parentheses x close parentheses equals x plus 2 dan g open parentheses x close parentheses equals 3 x minus 10.

b. Apakahopen parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses.

c. Sifat apakah yang dapat kalian temukan dari fungsi invers pada fungsi komposisi !

Pembahasan Soal:

Diketahui

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x plus 2 end cell row cell g open parentheses x close parentheses end cell equals cell 3 x minus 10 end cell end table

Dengan menggunakan konsep invers dan komposisi fungsi diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell x plus 2 end cell equals y row x equals cell y minus 2 end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell x minus 2 end cell end table  dan   table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals y row cell 3 x minus 10 end cell equals y row cell 3 x end cell equals cell y plus 10 end cell row x equals cell fraction numerator y plus 10 over denominator 3 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 10 over denominator 3 end fraction end cell end table

b. Akan ditunjukkan open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell row blank equals cell f to the power of negative 1 end exponent open parentheses fraction numerator x plus 10 over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator x plus 10 over denominator 3 end fraction minus 2 end cell row blank equals cell fraction numerator x plus 10 minus 6 over denominator 3 end fraction end cell row blank equals cell fraction numerator x plus 4 over denominator 3 end fraction end cell end table

Disisi lain

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x plus 2 close parentheses end cell row blank equals cell 3 open parentheses x plus 2 close parentheses minus 10 end cell row blank equals cell 3 x plus 6 minus 10 end cell row blank equals cell 3 x minus 4 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals y row cell 3 x minus 4 end cell equals y row cell 3 x end cell equals cell y plus 4 end cell row x equals cell fraction numerator y plus 4 over denominator 3 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 4 over denominator 3 end fraction end cell end table

Dengan demikian terbukti bahwa open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses.

c. Sehingga diperoleh sifat invers komposisi fungsi ssebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell row cell open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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