Pertanyaan

Diketahui f ( x ) = x − 3 2 x + 1 ​ , tentukan rumus fungsi f − 1 ( x + 2 ) !

Diketahui , tentukan rumus fungsi !

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

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Jawaban

rumus fungsi adalah .

rumus fungsi Error converting from MathML to accessible text. adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x plus 7 over denominator x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

Pembahasan

Dengan menggunakan konsep invers fungsi rasional diperoleh Misalkan maka Sehingga Dengan demikian rumus fungsi adalah .

Dengan menggunakan konsep invers fungsi rasional diperoleh

Misalkan f open parentheses x close parentheses equals y maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell fraction numerator 2 x plus 1 over denominator x minus 3 end fraction end cell equals y row cell 2 x plus 1 end cell equals cell y open parentheses x minus 3 close parentheses end cell row cell 2 x plus 1 end cell equals cell x y minus 3 y end cell row cell 2 x minus x y end cell equals cell negative 3 y minus 1 end cell row cell x open parentheses 2 minus y close parentheses end cell equals cell negative 3 y minus 1 end cell row x equals cell fraction numerator negative 3 y minus 1 over denominator 2 minus y end fraction end cell row x equals cell fraction numerator 3 y plus 1 over denominator y minus 2 end fraction comma space y not equal to 2 end cell end table

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 1 over denominator x minus 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x plus 2 close parentheses end cell equals cell fraction numerator 3 open parentheses x plus 2 close parentheses plus 1 over denominator open parentheses x plus 2 close parentheses minus 2 end fraction end cell row blank equals cell fraction numerator 3 x plus 6 plus 1 over denominator x plus 2 minus 2 end fraction end cell row blank equals cell fraction numerator 3 x plus 7 over denominator x end fraction comma space x not equal to 0 end cell end table

Dengan demikian rumus fungsi Error converting from MathML to accessible text. adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x plus 7 over denominator x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

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