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Fungsi ditentukan oleh dan dengan . Tentukan: b.

Pertanyaan

Fungsi begin mathsize 14px style f colon R rightwards arrow R comma space g colon R rightwards arrow R comma space dan space h colon R rightwards arrow R end style ditentukan oleh begin mathsize 14px style f left parenthesis x right parenthesis equals x minus 3 comma space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals x squared end style dan begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction space end styledengan size 14px x size 14px not equal to size 14px 3. Tentukan:

b. begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis space dan space left parenthesis f ring operator h right parenthesis left parenthesis x right parenthesis end style

Pembahasan Soal:

fungsi g(x) dapat ditentukan sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell x squared end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell x squared end cell row cell g left parenthesis x right parenthesis minus 3 end cell equals cell x squared end cell row cell g left parenthesis x right parenthesis end cell equals cell x squared plus 3 end cell end table end style

Selanjutnya, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis x minus 3 right parenthesis end cell row blank equals cell left parenthesis x minus 3 right parenthesis squared plus 3 space end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell x squared minus 6 x plus 12 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis h left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f open parentheses fraction numerator 2 x plus 1 over denominator x minus 3 end fraction close parentheses end cell row blank equals cell fraction numerator 2 x plus 1 over denominator x minus 3 end fraction minus 3 end cell row blank equals cell fraction numerator 2 x plus 1 minus 3 left parenthesis x minus 3 right parenthesis over denominator x minus 3 end fraction end cell row cell left parenthesis f ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator negative x plus 10 over denominator x minus 3 end fraction end cell end table end style

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 30 Maret 2021

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