Tentukan fungsi invers dari f(x)=2x−13x+4​, x=21​!

Pertanyaan

Tentukan fungsi invers dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style!

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Master Teacher

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Pembahasan

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style misalkan begin mathsize 14px style f open parentheses x close parentheses equals y end style maka begin mathsize 14px style x equals f to the power of negative 1 end exponent open parentheses y close parentheses end style sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction end cell row y equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction end cell row cell 2 x y minus y end cell equals cell 3 x plus 4 end cell row cell 2 x y minus 3 x end cell equals cell 4 plus y end cell row cell x left parenthesis 2 y minus 3 right parenthesis end cell equals cell y plus 4 end cell row x equals cell fraction numerator y plus 4 over denominator 2 y minus 3 end fraction end cell row cell f apostrophe left parenthesis y right parenthesis end cell equals cell fraction numerator y plus 4 over denominator 2 y minus 3 end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 4 over denominator 2 x minus 3 end fraction comma space x not equal to 3 over 2 end cell end table  

98

4.6 (3 rating)

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Jika f−1(x) adalah invers dari fungsi f(x)=3x−42x+5​, x=34​, maka nilai f−1(2)=....

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