Pertanyaan

Diketahui dua buah fungsi f ( x ) dan g ( x ) dengan f ( x ) = 3 x + 5 dan g ( x ) = 6 x − 5 x + 3 , x = 6 5 . Apabila ( g ∘ f ) − 1 ( x ) merupakan invers dari ( g ∘ f ) ( x ) , rumus fungsi dari adalah....

Diketahui dua buah fungsi $f (x)$ dan $g (x)$ dengan $f (x) = 3 x + 5$ dan $g (x) = \frac{x + 3}{6 x - 5}, x = \frac{5}{6}$ . Apabila $(g \circ f)^{- 1} (x)$ merupakan invers dari $(g \circ f) (x)$ , rumus fungsi dari adalah....

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Mencari open parentheses g ring operator f close parentheses left parenthesis x right parenthesis colon

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 3 x plus 5 close parentheses end cell row blank equals cell fraction numerator open parentheses 3 x plus 5 close parentheses plus 3 over denominator 6 open parentheses 3 x plus 5 close parentheses minus 5 end fraction end cell row blank equals cell fraction numerator 3 x plus 8 over denominator 18 x plus 30 minus 5 end fraction end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 8 over denominator 18 x plus 25 end fraction end cell end table$

Mencari open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis colon

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 8 over denominator 18 x plus 25 end fraction end cell row y equals cell fraction numerator 3 x plus 8 over denominator 18 x plus 25 end fraction end cell row cell y open parentheses 18 x plus 25 close parentheses end cell equals cell 3 x plus 8 end cell row cell 18 x y plus 25 y end cell equals cell 3 x plus 8 end cell row cell 18 x y minus 3 x end cell equals cell 8 minus 25 y end cell row cell x open parentheses 18 y minus 3 close parentheses end cell equals cell 8 minus 25 y end cell row x equals cell fraction numerator 8 minus 25 y over denominator 18 y minus 3 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator 8 minus 25 y over denominator 18 y minus 3 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 8 minus 25 x over denominator 18 x minus 3 end fraction end cell end table$

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