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Tentukan f−1(x) dari masing-masing fungsi berikut : a. f(x)= 3x−6  b. f(x)= 4−21​x  c. f(x)= 2x−3x+2​, x tidak sama dengan 23​.

Pertanyaan

Tentukan begin mathsize 14px style straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end style dari masing-masing fungsi berikut :

a. begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals space 3 straight x minus 6 end style 

b. Error converting from MathML to accessible text. 

c. Error converting from MathML to accessible text. begin mathsize 14px style straight x end style tidak sama dengan begin mathsize 14px style 3 over 2 end style.

F. Isyrofinnisak

Master Teacher

Jawaban terverifikasi

Jawaban

 table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 2 plus 3 x over denominator 2 x minus 1 end fraction comma x not equal to 1 half end cell end table.

Pembahasan

Dengan Konsep fungsi invers.

Misalkan begin mathsize 14px style straight y equals straight f left parenthesis straight x right parenthesis end style maka:

a. begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals space 3 straight x minus 6 end style,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis x right parenthesis end cell equals cell 3 x minus 6 end cell row y equals cell 3 x minus 6 end cell row cell 6 plus y end cell equals cell 3 x minus 6 plus 6 end cell row cell fraction numerator 6 plus y over denominator 3 end fraction end cell equals cell fraction numerator 3 x over denominator 3 end fraction end cell row cell fraction numerator 6 plus y over denominator 3 end fraction end cell equals x row cell straight f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 6 plus y over denominator 3 end fraction end cell row cell straight f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 6 plus x over denominator 3 end fraction end cell end table    

Jadi, straight f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 6 plus x over denominator 3 end fraction

b.Error converting from MathML to accessible text.,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis x right parenthesis end cell equals cell 4 minus 1 half x end cell row y equals cell 4 minus 1 half x end cell row cell left parenthesis negative 4 right parenthesis plus y end cell equals cell 4 minus 1 half x minus 4 end cell row cell y minus 4 end cell equals cell negative 1 half x space left parenthesis kedua space ruas space dibagi space left parenthesis negative 2 right parenthesis right parenthesis end cell row cell negative 2 left parenthesis y minus 4 right parenthesis end cell equals x row cell negative 2 y plus 8 end cell equals x row x equals cell 8 minus 2 y end cell row cell straight f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell 8 minus 2 y end cell row cell straight f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell 8 minus 2 x end cell end table   

Jadi, Error converting from MathML to accessible text. 

c. Error converting from MathML to accessible text.

Error converting from MathML to accessible text.     

Jadi table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 2 plus 3 x over denominator 2 x minus 1 end fraction comma x not equal to 1 half end cell end table.

31

3.5 (2 rating)

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Jika f(x)=x+52x+3​;x=−5 dan g(x)=3x+1. Tentukanlah f−1(g(x−31​)).

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