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Diketahui f(x)=x2+4x+4 dan g(x)=x2−4x+4. Rumus f(g(x))​+g(f(x))​=....

Pertanyaan

Diketahui  dan . Rumus  

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui  dan . Rumus  

kita sederhanakan dulu fungsinya,

 = begin mathsize 14px style open parentheses x plus 2 close parentheses squared end style 

 = begin mathsize 14px style open parentheses x minus 2 close parentheses squared end style 

kemudian tentukan dulu fungsi komposisinya:

size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 4 plus 2 right parenthesis end style to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis end style to the power of size 14px 2 size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px g size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared plus 4 x plus 4 minus 2 right parenthesis end style to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space  square root of size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px plus square root of size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px equals square root of begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis squared end style end root size 14px plus square root of size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 end root size 14px equals size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 size 14px plus size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px equals size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 8

jadi, jawabannya C

 

 

55

5.0 (4 rating)

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