Pertanyaan

Himpunan penyelesaian dari 1 < x 2 + 1 3 x 2 − 7 x + 8 ≤ 2 adalah ...

Himpunan penyelesaian dari $1 < \frac{3 x ^{2} - 7 x + 8}{x ^{2} + 1} \leq 2$ adalah ...

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Untuk : Benar untuk semua . Untuk : Nilai nol: Pembilang : Garis bilangan: Jadi,Himpunan penyelesaian dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Untuk $1 less than fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction$ :

$table attributes columnalign right center left columnspacing 0px end attributes row 1 less than cell fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction end cell row cell fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction end cell greater than 1 row cell fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction minus 1 end cell greater than 0 row cell fraction numerator 3 x squared minus 7 x plus 8 minus 1 open parentheses x squared plus 1 close parentheses over denominator x squared plus 1 end fraction end cell greater than 0 row cell fraction numerator 2 x squared minus 7 x plus 7 over denominator x squared plus 1 end fraction end cell greater than 0 row cell fraction numerator definit space positif over denominator definit space positif end fraction end cell greater than 0 row cell circled plus over circled plus end cell greater than 0 end table$

Benar untuk semua .

Untuk $fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction less or equal than 2$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction end cell less or equal than 2 row cell fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction minus 2 end cell less or equal than 0 row cell fraction numerator 3 x squared minus 7 x plus 8 minus 2 open parentheses x squared plus 1 close parentheses over denominator x squared plus 1 end fraction end cell less or equal than 0 row cell fraction numerator x squared minus 7 x plus 6 over denominator x squared plus 1 end fraction end cell less or equal than 0 row cell fraction numerator open parentheses x minus 1 close parentheses open parentheses x minus 6 close parentheses over denominator x squared plus 1 end fraction end cell less or equal than 0 row cell fraction numerator open parentheses x minus 1 close parentheses open parentheses x minus 6 close parentheses over denominator definit space positif end fraction end cell less or equal than 0 row cell fraction numerator open parentheses x minus 1 close parentheses open parentheses x minus 6 close parentheses over denominator circled plus end fraction end cell less or equal than 0 end table$

Nilai nol:

Pembilang : left parenthesis x minus 1 right parenthesis left parenthesis x minus 6 right parenthesis equals 0 rightwards arrow x equals 1 space atau space x equals 6

Garis bilangan:

Jadi, Himpunan penyelesaian dari $1 less than fraction numerator 3 x squared minus 7 x plus 8 over denominator x squared plus 1 end fraction less or equal than 2$ adalah left curly bracket 1 less or equal than x less or equal than 6 right curly bracket .

Dengan demikian, jawaban yang tepat adalah D.