Jika f(x)=5x−3, maka f(3)+(f∘f)−1(32)=....

Pertanyaan

Jika , maka ....

  1. 9

  2. 12

  3. 14

  4. 18

  5. 21

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Jika ,

kita tentukan dahulu :

begin mathsize 14px style f left parenthesis 3 right parenthesis equals 5 left parenthesis 3 right parenthesis minus 3 equals 15 minus 3 equals 12 end style

begin mathsize 14px style open parentheses f ring operator f close parentheses left parenthesis x right parenthesis equals f left parenthesis f left parenthesis x right parenthesis right parenthesis end style

               begin mathsize 14px style equals f left parenthesis 5 x minus 3 right parenthesis equals 5 left parenthesis 5 x minus 3 right parenthesis minus 3 equals 25 x minus 15 minus 3 equals 25 x minus 18 end style

kemudian kita tentukan inversnya :

size 14px y size 14px equals size 14px 25 size 14px x size 14px minus size 14px 18 size 14px y size 14px plus size 14px 18 size 14px equals size 14px 25 size 14px x fraction numerator size 14px y size 14px plus size 14px 18 over denominator size 14px 25 end fraction size 14px equals size 14px x size 14px left parenthesis size 14px f size 14px ring operator size 14px f size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px x size 14px plus size 14px 18 over denominator size 14px 25 end fraction size 14px left parenthesis size 14px f size 14px ring operator size 14px f size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px 32 size 14px right parenthesis size 14px equals fraction numerator size 14px 32 size 14px plus size 14px 18 over denominator size 14px 25 end fraction size 14px equals size 14px 50 over size 14px 25 size 14px equals size 14px 2

maka size 14px f size 14px left parenthesis size 14px 3 size 14px right parenthesis size 14px plus begin mathsize 14px style left parenthesis f ring operator f right parenthesis end style to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px 32 size 14px right parenthesis size 14px equals size 14px 12 size 14px plus size 14px 2 size 14px equals size 14px 14

jadi, jawabannya c

43

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Jika f(x)=2x+2, g(x)=3−x, dan h(x)=4x−1, maka (g∘f∘h)−1(x) yang tepat adalah ....

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