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Tentukan begin mathsize 14px style f open parentheses x close parentheses end style jika begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x plus 6 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 2 x plus 5 end style.

Jawaban:

Diketahui:

Fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x plus 6 end style.

Fungsi begin mathsize 14px style g open parentheses x close parentheses equals 2 x plus 5 end style.

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g open parentheses x close parentheses right parenthesis end cell row cell 4 x plus 6 end cell equals cell f left parenthesis 2 x plus 5 right parenthesis end cell end table end style

Misal: begin mathsize 14px style a equals 2 x plus 5 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 2 x plus 5 end cell row cell 2 x end cell equals cell a minus 5 end cell row x equals cell fraction numerator a minus 5 over denominator 2 end fraction end cell end table end style

Kemudian substitusi begin mathsize 14px style a end style dan begin mathsize 14px style x end style seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 3 x plus 5 close parentheses end cell equals cell 4 x plus 6 end cell row cell f open parentheses a close parentheses end cell equals cell 4 open parentheses fraction numerator a minus 5 over denominator 2 end fraction close parentheses plus 6 end cell row cell f open parentheses a close parentheses end cell equals cell 2 open parentheses a minus 5 close parentheses plus 6 end cell row cell f open parentheses a close parentheses end cell equals cell 2 a minus 10 plus 6 end cell row cell f open parentheses a close parentheses end cell equals cell 2 a minus 4 end cell end table end style

Maka, diperoleh begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 4 end style.

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