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Diketahui fungsi dan dengan dan . Tentukan: d.

Diketahui fungsi begin mathsize 14px style f colon space straight R rightwards arrow straight R end style dan Error converting from MathML to accessible text. dengan begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 2 end fraction end style.

Tentukan:

d. begin mathsize 14px style g ring operator g end style 

Jawaban:

Gunakan konsep komposisi fungsi untuk menentukan penyelesaian di atas.

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 2 end fraction end style

Akan ditentukan begin mathsize 14px style g ring operator g end style, perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses g ring operator g close parentheses open parentheses x close parentheses end cell equals cell g open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator 1 over denominator x plus 2 end fraction close parentheses end cell row blank equals cell fraction numerator 1 over denominator open parentheses begin display style fraction numerator 1 over denominator x plus 2 end fraction end style close parentheses plus 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator x plus 2 end fraction end style plus begin display style fraction numerator 2 open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 1 plus 2 x plus 4 over denominator x plus 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 2 x plus 5 over denominator x plus 2 end fraction end style end fraction end cell row blank equals cell 1 cross times fraction numerator x plus 2 over denominator 2 x plus 5 end fraction end cell row cell open parentheses g ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator x plus 2 over denominator 2 x plus 5 end fraction end cell end table end style  

Jadi, diperoleh begin mathsize 14px style open parentheses g ring operator g close parentheses open parentheses x close parentheses equals fraction numerator x plus 2 over denominator 2 x plus 5 end fraction end style.

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