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Diketahui fungsi f:R→R dan g:R→R dan f(x)=4x+3 dan g(x)=x+2. Tentukan: (g∘f)−1(2)

Pertanyaan

Diketahui fungsi begin mathsize 14px style f colon R rightwards arrow R space dan space g colon R rightwards arrow R end style dan begin mathsize 14px style f open parentheses x close parentheses equals 4 x plus 3 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x plus 2 end style. Tentukan:

begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses end style 

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses end style yaitu begin mathsize 14px style negative 3 over 4 end style.

Pembahasan

Nilai dari begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses end style dapat dicari dengan invers fungsi komposisi sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell 4 x plus 3 plus 2 end cell row blank equals cell 4 x plus 5 end cell row blank blank blank row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 4 x plus 5 end cell row y equals cell 4 x plus 5 end cell row cell 4 x end cell equals cell y minus 5 end cell row x equals cell fraction numerator y minus 5 over denominator 4 end fraction end cell row cell left parenthesis g ring operator f right parenthesis blank to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 5 over denominator 4 end fraction end cell row blank blank blank row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell fraction numerator x minus 5 over denominator 4 end fraction end cell row blank equals cell fraction numerator 2 minus 5 over denominator 4 end fraction end cell row blank equals cell negative 3 over 4 end cell end table end style

Jadi, nilai dari begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses end style yaitu begin mathsize 14px style negative 3 over 4 end style.

48

3.5 (4 rating)

Vallencia Haziba Sayyidah Nazah

Jawaban tidak sesuai

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