Pertanyaan

Jika f ( x ) = a x ,maka bentuk sederhana dari adalah ....

Jika $f (x) = a^{x}$ , maka bentuk sederhana dari $begin mathsize 14px style fraction numerator straight f open parentheses 3 straight x close parentheses plus straight f open parentheses negative 3 straight x close parentheses over denominator straight f open parentheses straight x close parentheses plus straight f open parentheses negative straight x close parentheses end fraction end style$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa Ingat bahwa , sehingga Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa

$begin mathsize 14px style fraction numerator straight f open parentheses 3 straight x close parentheses plus straight f open parentheses negative 3 straight x close parentheses over denominator straight f open parentheses straight x close parentheses plus straight f open parentheses negative straight x close parentheses end fraction equals fraction numerator straight a to the power of 3 straight x end exponent plus straight a to the power of negative 3 straight x end exponent over denominator straight a to the power of straight x plus straight a to the power of negative straight x end exponent end fraction end style$

Ingat bahwa , sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight f open parentheses 3 straight x close parentheses plus straight f open parentheses negative 3 straight x close parentheses over denominator straight f open parentheses straight x close parentheses plus straight f open parentheses negative straight x close parentheses end fraction end cell equals cell fraction numerator straight a to the power of 3 straight x end exponent plus straight a to the power of negative 3 straight x end exponent over denominator straight a to the power of straight x plus straight a to the power of negative straight x end exponent end fraction end cell row blank equals cell fraction numerator open parentheses straight a to the power of straight x close parentheses cubed plus open parentheses straight a to the power of negative straight x end exponent close parentheses cubed over denominator straight a to the power of straight x plus straight a to the power of negative straight x end exponent end fraction end cell row blank equals cell fraction numerator open parentheses straight a to the power of straight x plus straight a to the power of negative straight x end exponent close parentheses open parentheses straight a to the power of 2 straight x end exponent minus straight a to the power of straight x times straight a to the power of negative straight x end exponent plus straight a to the power of negative 2 straight x end exponent close parentheses over denominator straight a to the power of straight x plus straight a to the power of negative straight x end exponent end fraction end cell row blank equals cell straight a to the power of 2 straight x end exponent minus straight a to the power of straight x times straight a to the power of negative straight x end exponent plus straight a to the power of negative 2 straight x end exponent end cell row blank equals cell straight a to the power of 2 straight x end exponent minus straight a to the power of straight x times 1 over straight a to the power of straight x plus straight a to the power of negative 2 straight x end exponent end cell row blank equals cell straight a to the power of 2 straight x end exponent minus 1 plus straight a to the power of negative 2 straight x end exponent end cell row blank equals cell straight a to the power of 2 straight x end exponent plus straight a to the power of negative 2 straight x end exponent minus 1 end cell row blank blank blank end table end style$

Jadi, jawaban yang tepat adalah C.