Pertanyaan

Jika diketahui g ( x ) = 2 x − 4 dan ( f ∘ g ) ( x ) = 5 x − 9 7 x + 3 , nilai dari f ( 2 ) = ...

Jika diketahui $g (x) = 2 x - 4$ dan $(f \circ g) (x) = \frac{7 x + 3}{5 x - 9}$ , nilai dari $f (2)$ = ...

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Jawaban terverifikasi

Jawaban

nilai dari = 4

nilai dari

= 4

Pembahasan

Diketahui dan , misalkan maka Sehingga: Jadi, nilai dari = 4

Diketahui dan $begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator 7 x plus 3 over denominator 5 x minus 9 end fraction end style$ , misalkan maka $begin mathsize 14px style x equals fraction numerator y plus 4 over denominator 2 end fraction end style$

Sehingga:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 7 x plus 3 over denominator 5 x minus 9 end fraction end cell row cell f open parentheses 2 x minus 4 close parentheses end cell equals cell fraction numerator 7 x plus 3 over denominator 5 x minus 9 end fraction end cell row cell f open parentheses y close parentheses end cell equals cell fraction numerator 7 open parentheses begin display style fraction numerator y plus 4 over denominator 2 end fraction end style close parentheses plus 3 over denominator 5 open parentheses fraction numerator y plus 4 over denominator 2 end fraction close parentheses minus 9 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 y plus 28 plus 6 over denominator 2 end fraction end style over denominator begin display style fraction numerator 5 y plus 20 minus 18 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 7 y plus 34 over denominator 2 end fraction times fraction numerator 2 over denominator 5 y plus 2 end fraction end cell row blank equals cell fraction numerator 7 y plus 34 over denominator 5 y plus 2 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 7 x plus 34 over denominator 5 x plus 2 end fraction end cell row cell f open parentheses 2 close parentheses end cell equals cell fraction numerator 7 open parentheses 2 close parentheses plus 34 over denominator 5 open parentheses 2 close parentheses plus 2 end fraction end cell row blank equals 4 end table end style$

Jadi, nilai dari = 4