Pertanyaan

Jika f ( x ) = 4 x − 3 dan g ( x ) = x − 2 x + 1 , maka tentukan: a. f ∘ g ( x )

Jika $f (x) = 4 x - 3$ dan $g (x) = \frac{x + 1}{x - 2}$ , maka tentukan:

a. $f \circ g (x)$

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

.

f ring operator g open parentheses x close parentheses

$equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator italic x plus 10 over denominator italic x minus sign 2 end fraction end cell end table$ .

Pembahasan

Jika dan , maka adalah Jadi, .

Jika f open parentheses x close parentheses equals 4 x minus 3 dan $g open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x minus 2 end fraction$ , maka f ring operator g open parentheses x close parentheses adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator x plus 1 over denominator x minus 2 end fraction close parentheses end cell row blank equals cell 4 open parentheses fraction numerator x plus 1 over denominator x minus 2 end fraction close parentheses minus 3 end cell row blank equals cell fraction numerator 4 x plus 4 over denominator x minus 2 end fraction minus 3 end cell row blank equals cell fraction numerator 4 x plus 4 over denominator x minus 2 end fraction minus fraction numerator 3 open parentheses x minus 2 close parentheses over denominator x minus 2 end fraction end cell row blank equals cell fraction numerator 4 x plus 4 minus 3 x plus 6 over denominator x minus 2 end fraction end cell row blank equals cell fraction numerator x plus 10 over denominator x minus 2 end fraction end cell end table$

Jadi, f ring operator g open parentheses x close parentheses $equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator italic x plus 10 over denominator italic x minus sign 2 end fraction end cell end table$ .