Himpunan penyelesaian dari 1<x2+13x2−7x+8​≤2 adalah ...

Pertanyaan

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 ...

  1. left curly bracket x less or equal than 2 union x greater or equal than 3 right curly bracket 

  2. left curly bracket 2 less or equal than x less or equal than 3 right curly bracket 

  3. left curly bracket x less or equal than 1 union x greater or equal than 6 right curly bracket 

  4. left curly bracket 1 less or equal than x less or equal than 6 right curly bracket 

  5. left curly bracket x element of bold italic R right curly bracket 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

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 x.

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.

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