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Diketahui fungsi   dan . Fungsi invers dari  adala...

Diketahui fungsi  begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 1 end style dan begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 2 x minus 1 over denominator x plus 3 end fraction end style. Fungsi invers dari size 14px left parenthesis size 14px g size 14px ring operator size 14px f size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis negative 2 right parenthesis end style adalah ...

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Jawaban:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses 3 x plus 1 close parentheses end cell row cell space space space space space space space space space space space space space end cell equals cell fraction numerator 2 open parentheses 3 x plus 1 close parentheses over denominator open parentheses 3 x plus 1 close parentheses plus 3 end fraction end cell row cell space space space space space space space space space space space space space end cell equals cell fraction numerator 6 x plus 2 over denominator 3 x plus 4 end fraction end cell row cell m i s a l space y end cell equals cell fraction numerator 6 x plus 2 over denominator 3 x plus 4 end fraction end cell row cell y open parentheses 3 x plus 4 close parentheses end cell equals cell 6 x plus 2 end cell row cell 3 x y plus 4 y space end cell equals cell 6 x plus 2 end cell row cell 3 x y minus 6 x space end cell equals cell 2 minus 4 y end cell row cell x open parentheses 3 y minus 6 close parentheses end cell equals cell 2 minus 4 y end cell row x equals cell fraction numerator 2 minus 4 y over denominator 3 y minus 6 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 minus 4 x over denominator 3 x minus 6 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses end cell equals cell fraction numerator 2 minus 4 open parentheses negative 2 close parentheses over denominator 3 open parentheses negative 2 close parentheses minus 6 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 2 plus 8 over denominator negative 6 minus 6 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell negative 10 over 12 end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell negative 5 over 6 end cell row blank blank blank end table end style  

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