Roboguru

Diketahui  , , maka  = ....

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction end style , begin mathsize 14px style x not equal to 3 end style, maka begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style = ....

  1. begin mathsize 14px style fraction numerator x minus 3 over denominator 2 x plus 1 end fraction comma space x not equal to negative 1 half end style 

  2. fraction numerator size 14px 3 size 14px x size 14px plus size 14px 1 over denominator size 14px x size 14px minus size 14px 2 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px 2  

  3. fraction numerator size 14px 2 size 14px x size 14px plus size 14px 3 over denominator size 14px x size 14px minus size 14px 1 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px 1 

  4. fraction numerator size 14px 3 size 14px x size 14px minus size 14px 1 over denominator size 14px x size 14px plus size 14px 2 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px minus size 14px 2 

  5. fraction numerator size 14px 2 size 14px x size 14px minus size 14px 3 over denominator size 14px x size 14px plus size 14px 1 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px minus size 14px 1 

Pembahasan Soal:

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction end style 

Untuk mencari invers fungsi f, kita misalkan y = f(x) kemudian lakukan manipulasi aljabar sedemikian hingga diperoleh rumusan x dalam variabel y.

begin mathsize 14px style y equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction end style 

begin mathsize 14px style x y minus 3 y equals 2 x plus 1 end style 

begin mathsize 14px style x y minus 2 x equals 3 y plus 1 end style 

begin mathsize 14px style x open parentheses y minus 2 close parentheses equals 3 y plus 1 end style 

begin mathsize 14px style x equals fraction numerator 3 y plus 1 over denominator y minus 2 end fraction end style 

dengan syarat penyebut tidak nol.

begin mathsize 14px style y minus 2 not equal to 0 end style 

begin mathsize 14px style y not equal to 2 end style 

Jadi invers fungsi f adalah 

begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x plus 1 over denominator x minus 2 end fraction space comma space x not equal to 2 end style 

Jawaban yang benar B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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