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Diketahui . Jika nilai dari , maka ....

Pertanyaan

Diketahui begin mathsize 14px style straight f open parentheses straight x close parentheses equals straight g open parentheses straight x minus square root of 6 straight x minus 2 end root close parentheses end style. Jika nilai dari begin mathsize 14px style straight f to the power of straight apostrophe open parentheses 3 close parentheses equals 2 end style, maka begin mathsize 14px style straight g to the power of straight apostrophe open parentheses negative 1 close parentheses equals end style....

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R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

begin mathsize 14px style straight g to the power of straight apostrophe open parentheses negative 1 close parentheses equals 8 end style.

Pembahasan

Diketahui :

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Misalkan:

begin mathsize 14px style straight u equals 6 straight x minus 2 end style 

Maka,

begin mathsize 14px style straight u to the power of straight apostrophe equals 6 end style 

Sehingga jika kita misalkan begin mathsize 14px style square root of 6 straight x minus 2 end root equals straight k open parentheses straight x close parentheses end style maka turunan dari begin mathsize 14px style straight k open parentheses straight x close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight k open parentheses straight x close parentheses end cell equals cell square root of 6 straight x minus 2 end root end cell row cell straight k open parentheses straight x close parentheses end cell equals cell straight u to the power of 1 half end exponent end cell row cell straight k to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell 1 half straight u to the power of 1 half minus 1 end exponent times straight u to the power of straight apostrophe end cell row blank equals cell 1 half straight u to the power of negative 1 half end exponent times 6 end cell row blank equals cell 3 over straight u to the power of 1 half end exponent end cell row blank equals cell fraction numerator 3 over denominator square root of 6 straight x minus 2 end root end fraction end cell end table end style 

 

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight g left parenthesis straight x minus square root of 6 straight x minus 2 end root right parenthesis end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell straight g to the power of straight apostrophe left parenthesis straight x minus square root of 6 straight x minus 2 end root right parenthesis open parentheses 1 minus fraction numerator 3 over denominator square root of 6 straight x minus 2 end root end fraction close parentheses end cell row cell straight f to the power of straight apostrophe left parenthesis 3 right parenthesis end cell equals cell straight g to the power of straight apostrophe left parenthesis 3 minus square root of 6 open parentheses 3 close parentheses minus 2 end root right parenthesis open parentheses 1 minus fraction numerator 3 over denominator square root of 6 left parenthesis 3 right parenthesis minus 2 end root end fraction close parentheses end cell row 2 equals cell straight g to the power of straight apostrophe left parenthesis 3 minus 4 right parenthesis open parentheses 1 minus 3 over 4 close parentheses end cell row 2 equals cell straight g to the power of straight apostrophe left parenthesis negative 1 right parenthesis space 1 fourth end cell row 8 equals cell straight g to the power of straight apostrophe left parenthesis negative 1 right parenthesis end cell end table end style 

 

Jadi, begin mathsize 14px style straight g to the power of straight apostrophe open parentheses negative 1 close parentheses equals 8 end style.

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