Roboguru

Diketahui ,  dan  Tentukan

Diketahui begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 5 straight x minus 2 end stylebegin mathsize 14px style g left parenthesis straight x right parenthesis equals 3 minus x comma end style dan begin mathsize 14px style straight h left parenthesis straight x right parenthesis equals fraction numerator straight x over denominator straight x plus 1 end fraction. end style Tentukan begin mathsize 14px style left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis negative 2 right parenthesis factorial end style 

Jawaban:

Dengan menerapkan konsep komposisi 3 fungsi, maka diperoleh penyelesaian sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell equals cell straight g left parenthesis straight f left parenthesis straight h left parenthesis straight x right parenthesis right parenthesis right parenthesis end cell row blank equals cell straight g left parenthesis straight f left parenthesis fraction numerator straight x over denominator straight x plus 1 end fraction right parenthesis right parenthesis end cell row blank equals cell straight g left parenthesis 5 left parenthesis fraction numerator straight x over denominator straight x plus 1 end fraction right parenthesis minus 2 right parenthesis end cell row blank equals cell straight g left parenthesis fraction numerator 5 straight x over denominator straight x plus 1 end fraction minus 2 right parenthesis end cell row blank equals cell 3 minus left parenthesis fraction numerator 5 straight x over denominator straight x plus 1 end fraction minus 2 right parenthesis end cell row blank equals cell 3 minus fraction numerator 5 straight x over denominator straight x plus 1 end fraction plus 2 end cell row blank equals cell 5 minus fraction numerator 5 straight x over denominator straight x plus 1 end fraction end cell end table end style 

Fungsi begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 straight x over denominator straight x plus 1 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 left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell equals cell 5 minus fraction numerator 5 straight x over denominator straight x plus 1 end fraction end cell row cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis negative 2 right parenthesis end cell equals cell 5 minus fraction numerator 5 times left parenthesis negative 2 right parenthesis over denominator negative 2 plus 1 end fraction end cell row blank equals cell 5 minus fraction numerator negative 10 over denominator negative 1 end fraction end cell row blank equals cell 5 minus 10 end cell row blank equals cell negative 5 end cell end table end style 

Jadi, Nilai dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table end style

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