Pertanyaan

Fungsi f : R → R dan g : R → R dirumuskan dengan f ( x ) = x x − 1 , x  = 0 dan g ( x ) = x + 3 , fungsi ( g ∘ f ) − 1 ( x ) = ....

Fungsi $f : R \to R$ dan $g : R \to R$ dirumuskan dengan $f (x) = \frac{x - 1}{x}$ , $x \neq = 0$ dan $g (x) = x + 3$ , fungsi $(g \circ f)^{- 1} (x) =$ ....

$begin mathsize 14px style fraction numerator 4 minus 3 x over denominator x minus 1 end fraction comma space x not equal to 1 end style$
$begin mathsize 14px style fraction numerator 4 plus 3 x over denominator x plus 1 end fraction comma space x not equal to negative 1 end style$
$begin mathsize 14px style fraction numerator x minus 2 over denominator x end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 4 x minus 1 over denominator x end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 1 over denominator 4 minus x end fraction comma space x not equal to 4 end style$

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Klaim

F. Khansabyla

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Jadi, jawaban yang tepat adalah E.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator x minus 1 over denominator x end fraction close parentheses end cell row blank equals cell fraction numerator x minus 1 over denominator x end fraction plus 3 end cell row blank equals cell fraction numerator x minus 1 over denominator x end fraction plus fraction numerator 3 x over denominator x end fraction end cell row blank equals cell fraction numerator x minus 1 plus 3 x over denominator x end fraction end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 4 x minus 1 over denominator x end fraction end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals y row cell fraction numerator 4 x minus 1 over denominator x end fraction end cell equals y row cell 4 x minus 1 end cell equals cell x y end cell row cell 4 x minus x y end cell equals 1 row cell x open parentheses 4 minus y close parentheses end cell equals 1 row x equals cell fraction numerator 1 over denominator 4 minus y end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator 4 minus x end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah E.