Pertanyaan

Diketahui f ( x ) = x 2 + 2 x , g ( x ) = x − 5 dan h ( x ) = 2 − x x − 4 . Tentukan ( g ∘ f ∘ h ) ( 4 )

Diketahui $f (x) = x^{2} + 2 x, g (x) = x - 5 dan h (x) = \frac{x - 4}{2 - x}$ . Tentukan $(g \circ f \circ h) (4)$

A. Rahmawati

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses equals negative 4

open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses equals negative 4

Pembahasan

Diketahui : Ditanya : Penyelesaian Akan dicari nilai dari Jadi nilai dari adalah . Akan dicari nilai dari tetapi sebelumnya dicari nilai dari Jadi hasil dari . Akan dicari nilai dari . Jadi, nilai dari .

Diketahui :

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis space end cell equals cell space straight x ² space plus space 2 straight x space end cell row cell straight g left parenthesis straight x right parenthesis space end cell equals cell space straight x space minus space 5 space end cell row cell straight h left parenthesis straight x right parenthesis space end cell equals cell space fraction numerator open parentheses straight x minus 4 close parentheses over denominator open parentheses 2 minus straight x close parentheses end fraction end cell end table$

Ditanya :

Tentukan open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses

Penyelesaian

Akan dicari nilai dari open parentheses f ring operator h close parentheses open parentheses x close parentheses

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight f open parentheses straight h open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight f open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses squared plus 2 open parentheses fraction numerator straight x minus 4 over denominator 2 minus straight x end fraction close parentheses end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 2 straight x minus 8 over denominator 2 minus straight x end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 2 straight x minus 8 open parentheses 2 minus straight x close parentheses over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction plus fraction numerator 4 straight x minus 2 straight x squared minus 16 plus 8 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator straight x squared minus 8 straight x plus 16 minus 2 straight x squared plus 12 straight x minus 16 over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell end table$

Jadi nilai dari open parentheses f ring operator h close parentheses open parentheses x close parentheses adalah $fraction numerator negative x squared plus 4 x over denominator 4 minus 4 x plus x squared end fraction$ .

Akan dicari nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses tetapi sebelumnya dicari nilai dari

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight f ring operator straight h close parentheses open parentheses straight x close parentheses end cell row blank equals cell straight g open parentheses fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction close parentheses end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction minus 5 end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction minus fraction numerator 5 open parentheses negative straight x squared plus 4 straight x close parentheses over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator negative straight x squared plus 4 straight x plus 5 straight x squared minus 20 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell row blank equals cell fraction numerator 4 straight x squared minus 20 straight x over denominator 4 minus 4 straight x plus straight x squared end fraction end cell end table$

Jadi hasil dari $open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses x close parentheses equals fraction numerator 4 x squared minus 20 x over denominator 4 minus 4 x plus x squared end fraction$ .

Akan dicari nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses .

Jadi, nilai dari open parentheses straight g ring operator straight f ring operator straight h close parentheses open parentheses 4 close parentheses equals negative 4 .

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