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Diketahui . Jika  adalah fungsi invers , fungsi  a...

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x minus 2 end fraction comma x not equal to 2 end style. Jika begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style adalah fungsi invers begin mathsize 14px style f left parenthesis x right parenthesis end style, fungsi undefined adalah ...

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 1 over denominator x minus 2 end fraction end cell row y equals cell fraction numerator x plus 1 over denominator x minus 2 end fraction end cell row cell y left parenthesis x minus 2 right parenthesis end cell equals cell x plus 1 space end cell row cell x y minus 2 y end cell equals cell x plus 1 space end cell row cell x y minus x end cell equals cell 2 y plus 1 space end cell row cell x left parenthesis y minus 1 right parenthesis end cell equals cell 2 y plus 1 end cell row x equals cell fraction numerator 2 y plus 1 over denominator y minus 1 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 1 over denominator x minus 1 end fraction comma blank x not equal to 1 end cell end table end style

Jadi, begin mathsize 14px style bold italic f to the power of bold minus bold 1 end exponent begin bold style left parenthesis x right parenthesis end style bold equals fraction numerator bold 2 bold x bold plus bold 1 over denominator bold x bold minus bold 1 end fraction bold comma blank bold italic x bold not equal to bold 1 end style

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