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Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 1 plus x end root end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x minus 3 end style. Carilah:

c. nilai begin mathsize 14px style a end style jika begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis a right parenthesis equals 3 g left parenthesis a plus 6 right parenthesis end style.

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 1 plus x end root end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x minus 3 end style

begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals x squared minus 1 end style sehingga diperoleh :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f to the power of negative 1 end exponent open parentheses a close parentheses end cell equals cell 3 g open parentheses a plus 6 close parentheses end cell row cell a squared minus 1 end cell equals cell 3 open parentheses open parentheses a plus 6 close parentheses minus 3 close parentheses end cell row cell a squared minus 1 end cell equals cell 3 a plus 9 end cell row cell a squared minus 3 a minus 10 end cell equals 0 row cell open parentheses a minus 5 close parentheses open parentheses a plus 2 close parentheses end cell equals 0 row cell a equals 5 space end cell atau cell a equals negative 2 end cell end table end style

Jadi, begin mathsize 14px style a equals 5 space atau space a equals negative 2 end style.

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Diketahui fungsi f:R→R dan g:R→R dirumuskan dengan f(x)=xx−1​, untuk x=0 dan g(x)=x+3. Tentukanlah (g∘f(x))−1.

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