Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Black Craig. in South Africa
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( f \circ g(x) = 6x - 5 \)
Solución
1. We start with the definition of the composite function:
\[
(f \circ g)(x) = f(g(x))
\]
2. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3)
\]
3. Since \( f(x) = 3x + 4 \), replace \( x \) with \( 2x - 3 \):
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. Distribute and simplify:
\[
3(2x - 3) = 6x - 9
\]
Thus,
\[
f(2x - 3) = 6x - 9 + 4 = 6x - 5
\]
5. The final expression for the composite function is:
\[
(f \circ g)(x) = 6x - 5
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To find \( f \circ g(x) \), you need to substitute \( g(x) \) into \( f(x) \): 1. First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] 2. Now substitute \( g(x) \) into \( f(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] 3. Substitute \( 2x - 3 \) into \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, \( f \circ g(x) = 6x - 5 \).
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