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Diketahui fungsi dan , . Tentukan : b. dan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 3 x minus 1 end fraction end style, begin mathsize 14px style x not equal to 1 third end style. Tentukan :

b. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis end style dan begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis end style

  1. ... undefined 

  2. ... undefined 

Jawaban:

Pada fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 end style maka begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 2 x plus 3 end cell equals y row cell 2 x end cell equals cell y minus 3 end cell row x equals cell fraction numerator y minus 3 over denominator 2 end fraction end cell row jadi blank blank row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 3 over denominator 2 end fraction end cell end table end style 

 

Pada begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 3 x minus 1 end fraction end style, begin mathsize 14px style x not equal to 1 third end style. Maka begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 2 x plus 3 over denominator 3 x minus 1 end fraction end cell equals y row cell 2 x plus 3 end cell equals cell 3 y x minus y end cell row cell negative 2 x plus 3 y x end cell equals cell y plus 3 end cell row cell x open parentheses negative 2 plus 3 y close parentheses end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 3 y minus 2 end fraction end cell row jadi blank blank row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 3 over denominator 3 x minus 2 end fraction end cell end table end style 

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