Diberikan fungsi f(x)=x2−x+3 dan g(x)=3x−5. Maka: d. (gf​)(x)

Pertanyaan

Diberikan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus x plus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x minus 5 end style. Maka:

d. begin mathsize 14px style open parentheses f over g close parentheses left parenthesis x right parenthesis end style 

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 1 right parenthesis x plus 3 over denominator 3 x minus 5 end fraction end style.

Pembahasan

Pembagian begin mathsize 14px style f space dan space g end style ditulis begin mathsize 14px style f over g end style, didefinisikan sebagai begin mathsize 14px style open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end style dengan daerah asal begin mathsize 14px style D subscript begin inline style f over g end style end subscript equals D subscript f intersection D subscript g minus x left enclose g left parenthesis x right parenthesis equals 0 end enclose end style

Diketahui:

begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus x plus 3 g left parenthesis x right parenthesis equals 3 x minus 5 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f over g close parentheses left parenthesis x right parenthesis end cell equals cell fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator x squared minus x plus 3 over denominator 3 x minus 5 end fraction end cell row blank equals cell fraction numerator left parenthesis x minus 1 right parenthesis x plus 3 over denominator 3 x minus 5 end fraction end cell end table end style 

Jadi, nilai begin mathsize 14px style open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 1 right parenthesis x plus 3 over denominator 3 x minus 5 end fraction end style.

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