Jika f(x)=x−1x+1 dan (f∘g)(x)=1+x2 maka g(2)=...

Pertanyaan

Jika $f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x minus 1 end fraction$ dan $\left(f\circ g\right)\left(x\right)=1+\frac2x$ maka $g\left(2\right)=...$

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah B

Ingat!

$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$

Perhatikan perhitungan berikut ini!

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 1 plus 2 over x end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 1 plus 2 over x end cell row cell fraction numerator g open parentheses x close parentheses plus 1 over denominator g open parentheses x close parentheses minus 1 end fraction end cell equals cell 1 plus 2 over x end cell row cell fraction numerator g open parentheses x close parentheses plus 1 over denominator g open parentheses x close parentheses minus 1 end fraction end cell equals cell x over x plus 2 over x end cell row cell fraction numerator g open parentheses x close parentheses plus 1 over denominator g open parentheses x close parentheses minus 1 end fraction end cell equals cell fraction numerator x plus 2 over denominator x end fraction end cell end table$

Dengan mensubstitusi nilai $x=2$ , diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator g open parentheses x close parentheses plus 1 over denominator g open parentheses x close parentheses minus 1 end fraction end cell equals cell fraction numerator x plus 2 over denominator x end fraction end cell row cell fraction numerator g open parentheses 2 close parentheses plus 1 over denominator g open parentheses 2 close parentheses minus 1 end fraction end cell equals cell fraction numerator 2 plus 2 over denominator 2 end fraction end cell row cell fraction numerator g open parentheses 2 close parentheses plus 1 over denominator g open parentheses 2 close parentheses minus 1 end fraction end cell equals cell 4 over 2 end cell row cell fraction numerator g open parentheses 2 close parentheses plus 1 over denominator g open parentheses 2 close parentheses minus 1 end fraction end cell equals 2 row cell g open parentheses 2 close parentheses plus 1 end cell equals cell 2 open square brackets g open parentheses 2 close parentheses minus 1 close square brackets end cell row cell g open parentheses 2 close parentheses plus 1 end cell equals cell 2 g open parentheses 2 close parentheses minus 2 end cell row cell 1 plus 3 end cell equals cell 2 g open parentheses 2 close parentheses minus g open parentheses 2 close parentheses end cell row 4 equals cell g open parentheses 2 close parentheses end cell row cell g open parentheses 2 close parentheses end cell equals 4 end table$

Oleh karena itu, jawaban yang benar adalah B.

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