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Diketahui dan . Nilai dari adalah ....

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 5 end style dan begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals 3 x plus 2 end style. Nilai dari begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 11 right parenthesis end style adalah ....

  1. 7space 

  2. 6space

  3. 5space

  4. 4space

  5. 3space

Jawaban:

Diberikan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 5 end style dan fungsi komposisi begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals 3 x plus 2 end style.

Fungsi begin mathsize 14px style g left parenthesis x right parenthesis end style dapat dicari dengan langkah seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell equals cell 3 x plus 2 end cell row cell g left parenthesis 4 x minus 5 right parenthesis end cell equals cell 3 x plus 2 end cell end table end style

Dimisalkan

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 4 x minus 5 end cell row cell 4 x end cell equals cell a plus 5 end cell row x equals cell fraction numerator a plus 5 over denominator 4 end fraction end cell end table end style 

Dengan demikian 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis a right parenthesis end cell equals cell 3 open parentheses fraction numerator a plus 5 over denominator 4 end fraction close parentheses plus 2 end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator 3 a plus 15 plus 8 over denominator 4 end fraction end cell row cell g left parenthesis a right parenthesis end cell equals cell 3 over 4 a plus 23 over 4 end cell row cell g left parenthesis x right parenthesis end cell equals cell 3 over 4 x plus 23 over 4 end cell end table end style 

Invers dari fungsi begin mathsize 14px style g left parenthesis x right parenthesis end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 over 4 x plus 23 over 4 end cell row cell 3 over 4 x end cell equals cell y minus 23 over 4 end cell row x equals cell 4 over 3 times open parentheses y minus 23 over 4 close parentheses end cell row x equals cell 4 over 3 y minus 23 over 3 end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell 4 over 3 x minus 23 over 3 end cell end table end style 

Dengan demikian, nilai dari begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 11 right parenthesis end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent left parenthesis 11 right parenthesis end cell equals cell 4 over 3 times 11 minus 23 over 3 end cell row blank equals cell fraction numerator 44 minus 23 over denominator 3 end fraction end cell row blank equals cell 21 over 3 end cell row blank equals 7 end table end style 

Jadi, jawaban yang tepat adalah A.

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