Grafik fungsi g(x)=128×4x2x2−256 memotong sumbu X di titik ...

Pertanyaan

Grafik fungsi $g(x)=\frac{2^{x^2}}{128\times4^x}-256$ memotong sumbu X di titik ...

$left parenthesis negative 2 comma space 0 right parenthesis space dan space left parenthesis negative 3 comma space 0 right parenthesis$
$left parenthesis negative 2 comma space 0 right parenthesis space dan space left parenthesis 3 comma space 0 right parenthesis$
$left parenthesis negative 3 comma space 0 right parenthesis space dan space left parenthesis 5 comma space 0 right parenthesis$
$left parenthesis 2 comma space 0 right parenthesis space dan space left parenthesis negative 3 comma space 0 right parenthesis$
$left parenthesis 3 comma space 0 right parenthesis space dan space left parenthesis negative 5 comma space 0 right parenthesis$

Pembahasan Soal:

Cara mencari titik potong grafik dengan sumbu $straight X$ adalah dengan mencari nilai $x$ dari persamaan $g left parenthesis x right parenthesis equals 0$ .

Ingat juga sifat-sifat bilangan berpangkat berikut:

$a to the power of m over a to the power of n equals a to the power of m minus n end exponent$
$a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent$
$open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent$

$table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals 0 row cell fraction numerator 2 to the power of x squared end exponent over denominator 128 cross times 4 to the power of x end fraction minus 256 end cell equals 0 row cell fraction numerator 2 to the power of x squared end exponent over denominator 2 to the power of 7 cross times open parentheses 2 squared close parentheses to the power of x end fraction end cell equals 256 row cell fraction numerator 2 to the power of x squared end exponent over denominator 2 to the power of 7 cross times 2 to the power of 2 x end exponent end fraction end cell equals 256 row cell 2 to the power of x squared minus 2 x minus 7 end exponent end cell equals cell 2 to the power of 8 end cell end table$

Persamaan eksponen bentuk $a to the power of f left parenthesis x right parenthesis end exponent equals a to the power of m$ , dengan $a equals 2$ ; $f left parenthesis x right parenthesis equals x squared minus 2 x minus 7$ dan $m equals 8$ , diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 2 x minus 7 end cell equals 8 row cell x squared minus 2 x minus 15 end cell equals 0 row cell open parentheses x minus 5 close parentheses open parentheses x plus 3 close parentheses end cell equals 0 row x equals cell negative 3 space atau space x equals 5 end cell end table$

Jadi, fungsi tersebut memotong sumbu X di titik $left parenthesis negative 3 comma space 0 right parenthesis$ dan $open parentheses 5 comma space 0 close parentheses$ .

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Salim

Mahasiswa/Alumni Universitas Pelita Harapan

Terakhir diupdate 06 Oktober 2021