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Pertanyaan

Jika f ( x ) = 4 ( 2 x − 3 ) ​ , x > 2 3 ​ maka nilai dari 4 ⋅ f ( 2 x − 3 ) adalah ….

Jika ,   maka nilai dari  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 

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

jawaban yang benar adalah C.

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Pembahasan

Sehingga, Misalkan: Kemudian, hitung turunan pertama . Maka diperoleh Jadi, jawaban yang benar adalah C.

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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