Pertanyaan

Grafik y = x 2 − 4 x + 3 x 2 − 4 terletak di atas sumbu X untuk ...

Grafik $y = \frac{x ^{2} - 4}{x ^{2} - 4 x + 3}$ terletak di atas sumbu $X$ untuk ...

atau
atau atau
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semua nilai

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Grafik terletak di atas sumbu , maka . Bentuk umum pertidaksamaan rasional: Sehingga diperoleh: Pembuat nol: Pembilang Penyebut Syarat: Uji titik: Untuk interval , ambil . Untuk interval , ambil . Untuk interval , ambil . Untuk interval , ambil . Untuk interval , ambil . Garis bilangan: Karena pertidaksamaan bertanda " ", maka daerah penyelesaian berada pada interval yang bertanda atau bernilai positif. Grafik terletak di atas sumbu untuk atau atau . Jadi, jawaban yang tepat adalah C.

Grafik $y equals fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction$ terletak di atas sumbu , maka $fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction greater than 0$ .

Bentuk umum pertidaksamaan rasional:

$fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction greater than 0 semicolon space g open parentheses x close parentheses not equal to 0$

Sehingga diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell greater than 0 row cell fraction numerator x squared plus 2 x minus 2 x minus 4 over denominator x squared minus x minus 3 x plus 3 end fraction end cell greater than 0 row cell fraction numerator x open parentheses x plus 2 close parentheses minus 2 open parentheses x plus 2 close parentheses over denominator x open parentheses x minus 1 close parentheses minus 3 open parentheses x minus 1 close parentheses end fraction end cell greater than 0 row cell fraction numerator open parentheses x minus 2 close parentheses open parentheses x plus 2 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses x minus 1 close parentheses end fraction end cell greater than 0 end table$

Pembuat nol:

Pembilang

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals 0 row x equals 2 row blank blank blank row cell x plus 2 end cell equals 0 row x equals cell negative 2 end cell end table

Penyebut

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 3 end cell equals 0 row x equals 3 row blank blank blank row cell x minus 1 end cell equals 0 row x equals 1 end table

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 3 end cell not equal to 0 row x not equal to 3 row blank blank blank row cell x minus 1 end cell not equal to 0 row x not equal to 1 end table

Uji titik:

Untuk interval x less than negative 2 , ambil x equals negative 3 .

Untuk interval negative 2 less than x less than 1 , ambil x equals 0 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell equals cell fraction numerator 0 squared minus 4 over denominator 0 squared minus 4 open parentheses 0 close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator 0 minus 4 over denominator 0 minus 0 plus 3 end fraction end cell row blank equals cell negative 4 over 3 space open parentheses minus close parentheses end cell end table$

Untuk interval 1 less than x less than 2 , ambil x equals 3 over 2 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell equals cell fraction numerator open parentheses begin display style 3 over 2 end style close parentheses squared minus 4 over denominator open parentheses begin display style 3 over 2 end style close parentheses squared minus 4 open parentheses begin display style 3 over 2 end style close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator begin display style 9 over 4 end style minus 4 over denominator begin display style 9 over 4 end style minus 6 plus 3 end fraction end cell row blank equals cell fraction numerator negative begin display style 7 over 4 end style over denominator begin display style 9 over 4 end style minus begin display style 12 over 4 end style end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator 7 over denominator down diagonal strike 4 end fraction end style over denominator negative begin display style fraction numerator 3 over denominator down diagonal strike 4 end fraction end style end fraction end cell row blank equals cell 7 over 3 space open parentheses plus close parentheses end cell end table$

Untuk interval 2 less than x less than 3 , ambil x equals 5 over 2 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell equals cell fraction numerator open parentheses begin display style 5 over 2 end style close parentheses squared minus 4 over denominator open parentheses begin display style 5 over 2 end style close parentheses squared minus 4 open parentheses begin display style 5 over 2 end style close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator begin display style 25 over 4 end style minus 4 over denominator begin display style 25 over 4 end style minus 10 plus 3 end fraction end cell row blank equals cell fraction numerator begin display style 9 over 4 end style over denominator begin display style 25 over 4 end style minus begin display style 28 over 4 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 9 over denominator down diagonal strike 4 end fraction end style over denominator negative begin display style fraction numerator 3 over denominator down diagonal strike 4 end fraction end style end fraction end cell row blank equals cell negative 3 space open parentheses minus close parentheses end cell end table$

Untuk interval x greater than 3 , ambil x equals 4 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell equals cell fraction numerator 4 squared minus 4 over denominator 4 squared minus 4 open parentheses 4 close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator 16 minus 4 over denominator 16 minus 16 plus 3 end fraction end cell row blank equals cell 12 over 3 end cell row blank equals cell 4 space open parentheses plus close parentheses end cell end table$

Garis bilangan:

Karena pertidaksamaan bertanda " greater than ", maka daerah penyelesaian berada pada interval yang bertanda open parentheses plus close parentheses atau bernilai positif.

Grafik $y equals fraction numerator x squared minus 4 over denominator x squared minus 4 x plus 3 end fraction$ terletak di atas sumbu untuk x less than negative 2 atau 1 less than x less than 2 atau x greater than 3 .

Jadi, jawaban yang tepat adalah C.