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Diketahui fungsi . Tentukan invers fungsi

Diketahui fungsi begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 x minus 3 end fraction comma x not equal to 3 over 2 end style. Tentukan invers fungsi begin mathsize 14px style g end style 

Jawaban:

Rumus fungsi invers adalah sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator a x plus b over denominator c x plus d end fraction comma space x not equal to d over c end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator negative d x plus b over denominator c x minus a end fraction comma x not equal to a over c end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator negative left parenthesis negative 3 right parenthesis x plus 1 over denominator 2 x minus 1 end fraction comma x not equal to 1 half end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 1 over denominator 2 x minus 1 end fraction comma x not equal to 1 half end cell end table end style  

Jadi, invers dari g(x) adalah sebagai begin mathsize 14px style g apostrophe left parenthesis x right parenthesis equals fraction numerator 3 x plus 1 over denominator 2 x minus 1 end fraction comma x not equal to 1 half end style 

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