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Math  /  Algebra

Question13. Jika f(x)=2x2−5f(x)=2 x^{2}-5 dan g(x):3x+22g(x): \sqrt{3 x+22} maka (f∘g)−1(−3)(f \circ g)^{-1}(-3) adaiah...

Studdy Solution

STEP 1

1. Fungsi f(x)=2x2−5 f(x) = 2x^2 - 5 .
2. Fungsi g(x)=3x+22 g(x) = \sqrt{3x + 22} .
3. Kita diminta mencari nilai (f∘g)−1(−3)(f \circ g)^{-1}(-3).

STEP 2

1. Tentukan komposisi fungsi f∘g f \circ g .
2. Cari nilai x x yang membuat f(g(x))=−3 f(g(x)) = -3 .
3. Temukan nilai (f∘g)−1(−3)(f \circ g)^{-1}(-3).

STEP 3

Tentukan komposisi fungsi f∘g f \circ g :
(f∘g)(x)=f(g(x))=f(3x+22) (f \circ g)(x) = f(g(x)) = f(\sqrt{3x + 22})
Substitusi g(x) g(x) ke dalam f(x) f(x) :
f(3x+22)=2(3x+22)2−5 f(\sqrt{3x + 22}) = 2(\sqrt{3x + 22})^2 - 5

STEP 4

Sederhanakan ekspresi:
f(3x+22)=2(3x+22)−5 f(\sqrt{3x + 22}) = 2(3x + 22) - 5 f(3x+22)=6x+44−5 f(\sqrt{3x + 22}) = 6x + 44 - 5 f(3x+22)=6x+39 f(\sqrt{3x + 22}) = 6x + 39

STEP 5

Cari nilai x x yang membuat f(g(x))=−3 f(g(x)) = -3 :
6x+39=−3 6x + 39 = -3

STEP 6

Selesaikan persamaan:
6x+39=−3 6x + 39 = -3 6x=−3−39 6x = -3 - 39 6x=−42 6x = -42 x=−7 x = -7

STEP 7

Nilai (f∘g)−1(−3)(f \circ g)^{-1}(-3) adalah x=−7 x = -7 .
Nilai (f∘g)−1(−3)(f \circ g)^{-1}(-3) adalah:
−7 \boxed{-7}

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