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Diketahui fungsi f ( x ) = 2 x − 1 , dan g ( x ) = 6 x x − 4 ​ , x  = 0. Jika invers fungsi ( f ∘ g ) ( x ) = ( f ∘ g ) − 1 ( x ) dan invers fungsi ( g ∘ f ) ( x ) = ( g ∘ f ) − 1 ( x ) . Tentukan: b. ( g ∘ f ) − 1 ( x )

Diketahui fungsi  dan  Jika invers fungsi  dan invers fungsi . Tentukan:

b.        

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F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

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diperoleh .

diperoleh Error converting from MathML to accessible text..

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Menentukan Diperoleh , sehingga inversnya: Jadi, diperoleh .

Menentukan begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses. end style    

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 f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 2 x minus 1 close parentheses end cell row blank equals cell fraction numerator open parentheses 2 x minus 1 close parentheses minus 4 over denominator 6 open parentheses 2 x minus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction end cell end table end style  

Diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction end cell end table end style, sehingga inversnya:

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 y row cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction end cell equals y row cell 2 x minus 5 end cell equals cell y open parentheses 12 x minus 6 close parentheses end cell row cell 2 x minus 5 end cell equals cell 12 x y minus 6 y end cell row cell 2 x minus 12 x y end cell equals cell 5 minus 6 y end cell row cell x open parentheses 2 minus 12 y close parentheses end cell equals cell 5 minus 6 y end cell row x equals cell fraction numerator 5 minus 6 y over denominator 2 minus 12 y end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator 5 minus 6 y over denominator 2 minus 12 y 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 5 minus 6 x over denominator 2 minus 12 x end fraction end cell end table end style  

Jadi, diperoleh Error converting from MathML to accessible text..

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