Roboguru

Diketahui  dan . Fungsi komposisi

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 2 over denominator x minus 1 end fraction end style dan begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x plus 3 end fraction end style. Fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals.... end style 

  1. begin mathsize 14px style fraction numerator 4 x plus 7 over denominator x minus 2 end fraction end style 

  2. begin mathsize 14px style fraction numerator 4 x plus 7 over denominator x plus 3 end fraction end style 

  3. begin mathsize 14px style fraction numerator x plus 3 over denominator x minus 2 end fraction end style 

  4. begin mathsize 14px style fraction numerator 2 x minus 1 over denominator x plus 7 end fraction end style 

  5. begin mathsize 14px style fraction numerator x minus 2 over denominator 4 x plus 7 end fraction end style 

Jawaban:

begin mathsize 14px style 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 open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator 2 x plus 1 over denominator x plus 3 end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses fraction numerator 2 x plus 1 over denominator x plus 3 end fraction close parentheses plus 2 over denominator open parentheses fraction numerator 2 x plus 1 over denominator x plus 3 end fraction close parentheses minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 1 plus 2 open parentheses x plus 3 close parentheses over denominator up diagonal strike x plus 3 end strike end fraction end style over denominator begin display style fraction numerator 2 x plus 1 minus 1 open parentheses x plus 3 close parentheses over denominator up diagonal strike x plus 3 end strike end fraction end style end fraction end cell row blank equals cell fraction numerator 2 x plus 1 plus 2 x plus 6 over denominator 2 x plus 1 minus x minus 3 end fraction end cell row blank equals cell fraction numerator 4 x plus 7 over denominator x minus 2 end fraction end cell end table end style 

Jadi, jawaban yang tepat adalah A.

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