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Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 1 over denominator square root of x squared minus 2 end root end fraction end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator 1 over denominator square root of x squared plus 6 x plus 7 end root end fraction end style. Tentukan fungsi begin mathsize 14px style g open parentheses x plus 2 close parentheses end style.

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Pembahasan

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses fraction numerator 1 over denominator square root of open parentheses g open parentheses x close parentheses close parentheses squared minus 2 end root end fraction equals fraction numerator 1 over denominator square root of x squared plus 6 x plus 7 end root end fraction square root of open parentheses g open parentheses x close parentheses close parentheses squared minus 2 end root equals square root of x squared plus 6 x plus 7 end root open parentheses g open parentheses x close parentheses close parentheses squared minus 2 equals x squared plus 6 x plus 7 open parentheses g open parentheses x close parentheses close parentheses squared equals x squared plus 6 x plus 9 open parentheses g open parentheses x close parentheses close parentheses squared equals open parentheses x plus 3 close parentheses squared g open parentheses x close parentheses equals x plus 3 end style

Jadi, dapat ditentukan 

begin mathsize 14px style g open parentheses x plus 2 close parentheses equals open parentheses x plus 2 close parentheses plus 3 g open parentheses x plus 2 close parentheses equals x plus 5 end style

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Selesaikanlah soal berikut: Diketahui f(x)=2x+3 dan (f∘g)(x)=2x2+6x−7, maka g(x)=....

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