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Diketahui f ( x ) = x + 3 dan ( g ∘ f ) ( x ) = 2 x 2 + 4 x − 3 . Nilai dari g ( 2 ) adalah ....

Diketahui  dan . Nilai dari  adalah ....

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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nilai dari .

nilai dari begin mathsize 14px style g left parenthesis 2 right parenthesis equals negative 5 end style.

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Ingat bahwa, dan , maka Carilah invers fungsi dari . Diketahui , maka . maka maka Jadi nilai dari .

Ingat bahwa, begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis end style dan begin mathsize 14px style f left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis equals x end style, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f ring operator f to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis x right parenthesis end cell end table end style

Carilah invers fungsi dari begin mathsize 14px style f end style. Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals x plus 3 end style, maka

begin mathsize 14px style rightwards arrow y equals x plus 3 rightwards arrow x equals y minus 3 rightwards arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals x minus 3 end style

 begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals 2 x squared plus 4 x minus 3 end style. maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell open parentheses g ring operator f close parentheses left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 2 left parenthesis x minus 3 right parenthesis squared plus 4 left parenthesis x minus 3 right parenthesis minus 3 end cell row blank equals cell 2 left parenthesis x squared minus 6 x plus 9 right parenthesis plus 4 x minus 12 minus 3 end cell row blank equals cell 2 x squared minus 12 x plus 18 plus 4 x minus 15 end cell row blank equals cell 2 x squared minus 8 x plus 3 end cell end table end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 2 right parenthesis end cell equals cell 2 left parenthesis 2 right parenthesis squared minus 8 left parenthesis 2 right parenthesis plus 3 end cell row blank equals cell 8 minus 16 plus 3 end cell row blank equals cell negative 5 end cell end table end style

Jadi nilai dari begin mathsize 14px style g left parenthesis 2 right parenthesis equals negative 5 end style.

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