Diketahui f(x)=x+2 dan g(x)=3x−10. a. Tentukan fungsi invers : f(x), g(x), dan (f∘g)(x).

Pertanyaan

Diketahui $f\left(x\right)=x+2$ dan $g\left(x\right)=3x-10$ .

a. Tentukan fungsi invers : $f\left(x\right),\;g\left(x\right),\;\mathrm{dan}\;\left(f\circ g\right)\left(x\right)$ .

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

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Pembahasan

Dengan menggunakan konsep fungsi komposisi diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell x plus 2 end cell equals y row x equals cell y minus 2 end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell x minus 2 end cell end table

Dengan demikian f to the power of negative 1 end exponent open parentheses x close parentheses equals x minus 2 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals y row cell 3 x minus 10 end cell equals y row cell 3 x end cell equals cell y plus 10 end cell row x equals cell fraction numerator y plus 10 over denominator 3 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 10 over denominator 3 end fraction end cell end table$

Dengan demikian Error converting from MathML to accessible text. .

Dengan menggunakan konsep komposisi fungsi diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 3 x minus 10 close parentheses end cell row blank equals cell 3 x minus 10 plus 2 end cell row blank equals cell 3 x minus 8 end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals y row cell 3 x minus 8 end cell equals y row cell 3 x end cell equals cell y plus 8 end cell row blank blank blank row x equals cell fraction numerator y plus 8 over denominator 3 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 8 over denominator 3 end fraction end cell end table$

Dengan demikian Error converting from MathML to accessible text. .