Pertanyaan

Jika f ( x ) = 2 x − 1 , g ( x ) = x 2 + 2 , dan h ( x ) = x − 1 1 , fungsi komposisi ( g ∘ h ∘ f ) ( x ) = ... .

Jika $f (x) = 2 x - 1$ , $g (x) = x^{2} + 2$ , dan $h (x) = \frac{1}{x - 1}$ , fungsi komposisi $(g \circ h \circ f) (x) = ... .$

$fraction numerator 8 x squared minus 16 x plus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$
$fraction numerator 8 x squared plus 16 x minus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$
$fraction numerator 8 x squared minus 16 x minus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$
$fraction numerator negative 8 x squared plus 16 x minus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$
$fraction numerator negative 8 x squared minus 16 x plus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Diketahui , , dan . Fungi komposisi sebagai berikut. Fungsi komposisi . Oleh karena itu, jawaban yang benar adalah A.

Diketahui f open parentheses x close parentheses equals 2 x minus 1 , g open parentheses x close parentheses equals x squared plus 2 , dan $h open parentheses x close parentheses equals fraction numerator 1 over denominator x minus 1 end fraction$ . Fungi komposisi open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses end cell equals cell open parentheses g ring operator h close parentheses open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell open parentheses g ring operator h close parentheses open parentheses 2 x minus 1 close parentheses end cell row blank equals cell g open parentheses h open parentheses 2 x minus 1 close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator 1 over denominator open parentheses 2 x minus 1 close parentheses minus 1 end fraction close parentheses end cell row blank equals cell g open parentheses fraction numerator 1 over denominator 2 x minus 1 minus 1 end fraction close parentheses end cell row blank equals cell g open parentheses fraction numerator 1 over denominator 2 x minus 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 over denominator 2 x minus 2 end fraction close parentheses squared plus 2 end cell row blank equals cell 1 over open parentheses 2 x minus 2 close parentheses squared plus 2 end cell row blank equals cell fraction numerator 1 over denominator open parentheses 2 x minus 2 close parentheses open parentheses 2 x minus 2 close parentheses end fraction plus 2 end cell row blank equals cell fraction numerator 1 over denominator 4 x squared minus 4 x minus 4 x plus 4 end fraction plus 2 end cell row blank equals cell fraction numerator 1 over denominator 4 x squared minus 8 x plus 4 end fraction plus 2 end cell row blank equals cell fraction numerator 1 over denominator 4 x squared minus 8 x plus 4 end fraction plus fraction numerator 2 open parentheses 4 x squared minus 8 x plus 4 close parentheses over denominator 4 x squared minus 8 x plus 4 end fraction end cell row blank equals cell fraction numerator 1 plus 8 x squared minus 16 x plus 8 over denominator 4 x squared minus 8 x plus 4 end fraction end cell row blank equals cell fraction numerator 8 x squared minus 16 x plus 9 over denominator 4 x squared minus 8 x plus 4 end fraction end cell end table$

Fungsi komposisi $open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 8 x squared minus 16 x plus 9 over denominator 4 x squared minus 8 x plus 4 end fraction$ .

Oleh karena itu, jawaban yang benar adalah A.