Pertanyaan

Tentukanlah interval di mana grafik fungsi y = 2 4 x + 2 berada di bawah grafik dari fungsi y = 2 3 x − 1 1 .

Tentukanlah interval di mana grafik fungsi $y = 2 4^{x + 2}$ berada di bawah grafik dari fungsi $y = \frac{1}{2 ^{3 x - 1}}$ .

S. Nur

Master Teacher

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interval fungsi tersebut adalah .

interval fungsi tersebut adalah x less than negative 1

Pembahasan

Diketahui: Grafik fungsi berada di bawah grafik fungsi . Ditanya: Interval grafik tersebut Grafik fungsi berada di bawah grafik fungsi apabila . Karena basis pertidaksamaan di atas lebih dari 1, maka: Jadi, interval fungsi tersebut adalah .

Diketahui:

Grafik fungsi y equals 2 square root of 4 to the power of x plus 2 end exponent end root berada di bawah grafik fungsi y equals square root of 1 over 2 to the power of 3 x minus 1 end exponent end root .

Ditanya:

Interval grafik tersebut

Grafik fungsi y subscript 1 equals 2 square root of 4 to the power of x plus 2 end exponent end root berada di bawah grafik fungsi y subscript 2 equals square root of 1 over 2 to the power of 3 x minus 1 end exponent end root apabila y subscript 1 less than y subscript 2 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript 1 end cell less than cell y subscript 2 end cell row cell 2 square root of 4 to the power of x plus 2 end exponent end root end cell less than cell square root of 1 over 2 to the power of 3 x minus 1 end exponent end root end cell row cell 2 open parentheses 4 to the power of x plus 2 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell less than cell open parentheses 1 over 2 to the power of 3 x minus 1 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row cell 2 open parentheses open parentheses 2 squared close parentheses to the power of x plus 2 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell less than cell open parentheses 2 to the power of negative open parentheses 3 x minus 1 close parentheses end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row cell 2 open parentheses 2 to the power of 2 x plus 4 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell less than cell open parentheses 2 to the power of negative 3 x plus 1 end exponent close parentheses to the power of begin inline style 1 half end style end exponent end cell row cell 2 open parentheses 2 to the power of x plus 2 end exponent close parentheses end cell less than cell open parentheses 2 to the power of begin inline style fraction numerator negative 3 x plus 1 over denominator 2 end fraction end style end exponent close parentheses end cell row cell 2 to the power of 1 open parentheses 2 to the power of x plus 2 end exponent close parentheses end cell less than cell open parentheses 2 to the power of begin inline style fraction numerator negative 3 x plus 1 over denominator 2 end fraction end style end exponent close parentheses end cell row cell open parentheses 2 to the power of x plus 2 plus 1 end exponent close parentheses end cell less than cell open parentheses 2 to the power of begin inline style fraction numerator negative 3 x plus 1 over denominator 2 end fraction end style end exponent close parentheses end cell row cell open parentheses 2 to the power of x plus 3 end exponent close parentheses end cell less than cell open parentheses 2 to the power of begin inline style fraction numerator negative 3 x plus 1 over denominator 2 end fraction end style end exponent close parentheses end cell end table$

Karena basis pertidaksamaan di atas lebih dari 1, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 to the power of x plus 3 end exponent close parentheses end cell less than cell open parentheses 2 to the power of begin inline style fraction numerator negative 3 x plus 1 over denominator 2 end fraction end style end exponent close parentheses end cell row cell x plus 3 end cell less than cell negative fraction numerator 3 x plus 1 over denominator 2 end fraction end cell row cell 2 x plus 6 end cell less than cell negative 3 x plus 1 end cell row cell 2 x plus 3 x end cell less than cell 1 minus 6 end cell row cell 5 x end cell less than cell negative 5 end cell row x less than cell negative 1 end cell end table$

Jadi, interval fungsi tersebut adalah x less than negative 1 .

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