Pregunta
6) Find \( (f \circ g)(x) \) when \( f(x)=-3 x^{2} \) and \( g(x)=7 x+4 \)
Ask by Gordon Hamilton. in Qatar
Feb 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(f ∘ g)(x) = -3(7x + 4)² or -147x² - 168x - 48
Solución
To find (f ∘ g)(x), substitute g(x) into f(x):
f(x) = -3x²
g(x) = 7x + 4
Thus,
(f ∘ g)(x) = f(g(x)) = -3(7x + 4)²
If desired, you can expand the squared term:
(7x + 4)² = 49x² + 56x + 16
Then,
-3(49x² + 56x + 16) = -147x² - 168x - 48
So, the composition is:
(f ∘ g)(x) = -3(7x + 4)², which can also be written as -147x² - 168x - 48.
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Simplifique esta solución Extra Insights
To find \( (f \circ g)(x) \), we first need to substitute the function \( g(x) \) into \( f(x) \). We know that \( f(x) = -3x^2 \) and \( g(x) = 7x + 4 \). 1. First, we find \( g(x) \): \[ g(x) = 7x + 4 \] 2. Next, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(7x + 4) = -3(7x + 4)^2 \] 3. Now, we need to expand \( (7x + 4)^2 \): \[ (7x + 4)^2 = 49x^2 + 56x + 16 \] 4. Substitute this back into \( f(g(x)) \): \[ f(7x + 4) = -3(49x^2 + 56x + 16) \] 5. Distribute the \(-3\): \[ f(7x + 4) = -147x^2 - 168x - 48 \] So, \( (f \circ g)(x) = -147x^2 - 168x - 48 \).
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