Pertanyaan

Diketahui f ( x ) = x + 3 2 x − 5 , x  = − 3 dan g ( x ) = x 2 Fungsi ( f ∘ g ) − 1 ( x ) adalah...

Diketahui $f (x) = \frac{2 x - 5}{x + 3}, x \neq = - 3$ dan $g (x) = \frac{2}{x}$

Fungsi $(f \circ g)^{- 1} (x)$ adalah...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

fungsi adalah

fungsi

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table

adalah $table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 2 x plus 4 over denominator 3 x plus 5 end fraction comma space x end cell not equal to cell negative 5 over 3 end cell end table$

Pembahasan

Diketahui dan , maka: Rumus invers fungsi adalah maka: Jadi, fungsi adalah

Diketahui $f left parenthesis x right parenthesis equals fraction numerator 2 x minus 5 over denominator x plus 3 end fraction comma space x not equal to negative 3$ dan g left parenthesis x right parenthesis equals 2 over x , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell fraction numerator 2 open parentheses begin display style 2 over x end style close parentheses minus 5 over denominator begin display style 2 over x end style plus 3 end fraction end cell row blank equals cell fraction numerator begin display style 4 over x end style minus 5 over denominator 2 over x plus 3 end fraction cross times x over x end cell row blank equals cell fraction numerator 4 minus 5 x over denominator 2 plus 3 x end fraction comma space x not equal to negative 2 over 3 end cell row blank blank blank row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 4 minus 5 x over denominator 2 plus 3 x end fraction end cell row blank blank blank end table$

Rumus invers fungsi $f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction comma x table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell d over a end cell end table$ adalah $f left parenthesis x right parenthesis to the power of negative 1 end exponent equals fraction numerator negative d x plus b over denominator c x minus a end fraction comma x table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a over c end cell end table$

maka:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 minus 5 x over denominator 2 plus 3 x end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 2 x plus 4 over denominator 3 x plus 5 end fraction end cell end table comma table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table$

Jadi, fungsi adalah $table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 2 x plus 4 over denominator 3 x plus 5 end fraction comma space x end cell not equal to cell negative 5 over 3 end cell end table$