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f(x)=x2−1​f(x)=x2+1​  maka (f∘g)−1(x)+(g∘f)−1(x) adalah ....

Pertanyaan

begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x squared minus 1 end root f left parenthesis x right parenthesis equals square root of x squared plus 1 end root end style 

maka begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style adalah ....

  1. begin mathsize 14px style 2 x end style 

  2. size 14px 2 size 14px x size 14px plus size 14px 1 

  3. begin mathsize 14px style x squared end style 

  4. begin mathsize 14px style x squared plus 1 end style 

  5. begin mathsize 14px style x to the power of 4 minus 1 end style 

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Pada soal yang diberikan, kedua fungsinya ditulis begin mathsize 14px style f left parenthesis x right parenthesis end style seharusnya salah satunya adalah fungsi size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis. Kita misalkan fungsi yang kedua adalah undefined, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell square root of x squared minus 1 end root end cell row y equals cell square root of x squared minus 1 end root end cell row cell y squared end cell equals cell x squared minus 1 end cell row cell x squared end cell equals cell y squared plus 1 end cell row x equals cell square root of y squared plus 1 end root end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell square root of x squared plus 1 end root end cell row blank blank blank row cell g left parenthesis x right parenthesis end cell equals cell square root of x squared plus 1 end root end cell row y equals cell square root of x squared plus 1 end root end cell row cell y squared end cell equals cell x squared plus 1 end cell row cell x squared end cell equals cell y squared minus 1 end cell row x equals cell square root of y squared minus 1 end root end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell square root of x squared minus 1 end root end cell end table end style  

sehingga diperoleh:

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

sehingga diperoleh:

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 x right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals x row blank equals cell 2 x end cell end table end style

Jadi, jawaban yang benar adalah A.

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