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Jika begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 1 end style dan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px 2 size 14px x size 14px minus size 14px 3, fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals horizontal ellipsis end style 

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Jawaban:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 1 end style dan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px 2 size 14px x size 14px minus size 14px 3. Fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end style dapat dihitung seperti berikut, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f left parenthesis 2 x minus 3 right parenthesis end cell row blank equals cell 4 left parenthesis 2 x minus 3 right parenthesis minus 1 end cell row blank equals cell 8 x minus 12 minus 1 end cell row blank equals cell 8 x minus 13 end cell end table end style 

Bentuk umum invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals a x plus b end style adalah

begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus b over denominator a end fraction comma space a not equal to 0 end style.

Oleh karena itu, fungsi invers dari begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals 8 x minus 13 end style yaitu

begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus left parenthesis negative 13 right parenthesis over denominator 8 end fraction equals fraction numerator x plus 13 over denominator 8 end fraction end style 

begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals fraction numerator 3 plus 13 over denominator 8 end fraction equals 16 over 8 equals 2 end style 

Dengan demikian, nilai dari fungsi begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end style adalah begin mathsize 14px style 2 end style.

Jadi, jawaban yang tepat adalah E.

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