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Jika begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fourth root of left parenthesis 2 straight x minus 3 right parenthesis end root end style,  begin mathsize 14px style straight x greater than 3 over 2 end style maka nilai dari begin mathsize 14px style 4 times straight f to the power of apostrophe left parenthesis 2 straight x minus 3 right parenthesis end style adalah ….

  1. begin mathsize 14px style fraction numerator 1 over denominator 4 fourth root of open parentheses 2 straight x minus 3 close parentheses end root end fraction end style

  2. begin mathsize 14px style fraction numerator 4 over denominator fourth root of open parentheses 2 x minus 3 close parentheses cubed end root end fraction end style 

  3. begin mathsize 14px style fraction numerator 4 over denominator fourth root of open parentheses 4 straight x minus 9 close parentheses cubed end root end fraction end style  

  4. begin mathsize 14px style fraction numerator 1 over denominator 4 fourth root of open parentheses 4 x minus 9 close parentheses cubed end root end fraction end style 

  5. begin mathsize 14px style fraction numerator 1 over denominator fourth root of open parentheses 4 x minus 9 close parentheses cubed end root end fraction end style 

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

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 fourth root of 2 straight x minus 3 end root end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell left parenthesis 2 straight x minus 3 right parenthesis to the power of 1 fourth end exponent space end cell row cell straight f left parenthesis 2 straight x minus 3 right parenthesis end cell equals cell left parenthesis 2 left parenthesis 2 straight x minus 3 right parenthesis minus 3 right parenthesis to the power of 1 fourth end exponent space end cell row space equals cell left parenthesis 4 straight x minus 9 right parenthesis to the power of 1 fourth end exponent end cell end table end style    

Sehingga,

begin mathsize 14px style straight f left parenthesis 2 straight x minus 3 right parenthesis equals left parenthesis 4 straight x minus 9 right parenthesis to the power of 1 fourth end exponent end style 

Misalkan:

begin mathsize 14px style straight u equals 4 straight x minus 9 rightwards arrow straight u to the power of apostrophe equals 4 end style 

Kemudian, hitung turunan pertama begin mathsize 14px style straight f left parenthesis 2 straight x minus 3 right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis 2 straight x minus 3 right parenthesis end cell equals cell straight u to the power of 1 fourth end exponent end cell row cell straight f to the power of apostrophe left parenthesis 2 straight x minus 3 right parenthesis end cell equals cell 1 fourth straight u to the power of 1 fourth minus 1 end exponent times straight u to the power of apostrophe end cell row blank equals cell 1 fourth straight u to the power of 3 over 4 end exponent times 4 end cell row blank equals cell 1 over straight u to the power of begin display style 3 over 4 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator fourth root of left parenthesis 4 straight x minus 9 right parenthesis cubed end root end fraction end cell end table end style 

 

Maka diperoleh

begin mathsize 14px style 4 times straight f to the power of apostrophe left parenthesis 2 straight x minus 3 right parenthesis equals fraction numerator 4 over denominator fourth root of left parenthesis 4 straight x minus 9 right parenthesis cubed end root end fraction end style  

Jadi, jawaban yang benar adalah C.

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