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Diketahui fungsi  dan . Tentukan nilai dari  adala...

Diketahui fungsi f left parenthesis x right parenthesis equals x minus 5 dan g left parenthesis x right parenthesis equals 3 x plus 2. Tentukan nilai dari left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis adalah ...

Jawaban:

Diketahui : f left parenthesis x right parenthesis equals x minus 5g left parenthesis x right parenthesis equals 3 x plus 2 

Jika f left parenthesis x right parenthesis equals y maka f to the power of negative 1 end exponent left parenthesis y right parenthesis equals x 

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x minus 5 end cell row x equals cell y plus 5 end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell y plus 5 end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell x plus 5 end cell end table 

Jika g left parenthesis x right parenthesis equals y maka g to the power of negative 1 end exponent left parenthesis y right parenthesis equals x 

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x plus 2 end cell row cell 3 x end cell equals cell y minus 2 end cell row x equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 2 over denominator 3 end fraction end cell end table  

Dengan menggunakan sifat invers fungsi komposisi maka :space 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell left parenthesis straight g to the power of negative 1 end exponent ring operator straight f to the power of negative 1 end exponent right parenthesis left parenthesis straight x right parenthesis end cell row blank equals cell straight g to the power of negative 1 end exponent left parenthesis straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis right parenthesis end cell row blank equals cell straight g to the power of negative 1 end exponent left parenthesis straight x plus 5 right parenthesis end cell row blank equals cell fraction numerator left parenthesis straight x plus 5 right parenthesis minus 2 over denominator 3 end fraction end cell row blank equals cell fraction numerator straight x plus 3 over denominator 3 end fraction end cell end table 

sehinggaspace 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell fraction numerator 3 plus 3 over denominator 3 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table 

Jadi, nilai dari left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis adalah 3.

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