Jika f(x)=x2+2x−2 dan g(x)=x2+3, maka (g∘f)(x)−g(x)−(g∘f)(x)=....

Pertanyaan

Jika $\style{font-size:14px}{f\left(x\right)=\sqrt{x^2+2x-2}}$ dan $\style{font-size:14px}{g\left(x\right)=x^2+3}$ , maka $\style{font-size:14px}{\left(g\circ f\right)\left(x\right)-g\left(x\right)-\sqrt{\left(g\circ f\right)\left(x\right)}=....}$

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Pembahasan:

Jika dan

kita cari dulu komposisi fungsinya,

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

$begin mathsize 14px style equals g open parentheses square root of x squared plus 2 x minus 2 end root close parentheses equals open parentheses square root of x squared plus 2 x minus 2 end root close parentheses squared plus 3 equals x squared plus 2 x minus 2 plus 3 equals x squared plus 2 x plus 1 end style$

Kemudian bentuk diatas bisa difaktorkan menjadi :

$begin mathsize 14px style x squared plus 2 x plus 1 equals left parenthesis x plus 1 right parenthesis squared end style$

sedemikian sehingga:

$begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis minus g left parenthesis x right parenthesis minus square root of open parentheses g ring operator f close parentheses left parenthesis x right parenthesis end root equals x squared plus 2 x plus 1 minus left parenthesis x squared plus 3 right parenthesis minus square root of x squared plus 2 x plus 1 end root end style$

$begin mathsize 14px style equals 2 x minus 2 minus square root of open parentheses x plus 1 close parentheses squared end root equals 2 x minus 2 minus left parenthesis x plus 1 right parenthesis equals x minus 3 end style$

jadi, jawabannya D

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Terakhir diupdate 05 Oktober 2021