Roboguru

Diketahui dan . Nilai dari adalah...

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals x minus 5 end style dan begin mathsize 14px style space g left parenthesis x right parenthesis equals 2 x plus 6 end style. Nilai dari begin mathsize 14px style open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses 5 close parentheses end style adalah...

Jawaban:

Ingat kembali sifat invers fungsi komposisi:

space left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis space

Maka yang perlu kita tentukan terlebih dahulu adalah begin mathsize 14px style space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell open parentheses g left parenthesis x right parenthesis close parentheses minus 5 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell open parentheses 2 x plus 6 close parentheses minus 5 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 2 x plus 1 end cell end table end style

Kemudian kita menetukan undefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 2 x plus 1 end cell row y equals cell 2 x plus 1 end cell row cell 2 x end cell equals cell y minus 1 end cell row x equals cell fraction numerator y minus 1 over denominator 2 end fraction end cell row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 1 over denominator 2 end fraction end cell end table end style

sehingga

begin mathsize 14px style 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 5 right parenthesis end cell equals cell fraction numerator 5 minus 1 over denominator 2 end fraction end cell row blank equals cell 4 over 2 end cell row blank equals 2 end table end style

Jadi, nilai begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 5 right parenthesis end cell end table end style adalah 2

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