Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Li Li. in Denmark
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( f \circ g(x) = 6x - 5 \)
Solución
To find the composition of the functions \( f \) and \( g \), denoted as \( f \circ g(x) \), follow these steps:
**Given:**
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
\]
**Step 1: Understand Composition**
\[
f \circ g(x) = f(g(x))
\]
This means you first apply \( g \) to \( x \), and then apply \( f \) to the result of \( g(x) \).
**Step 2: Substitute \( g(x) \) into \( f \)**
\[
f(g(x)) = f(2x - 3)
\]
**Step 3: Apply the function \( f \) to \( 2x - 3 \)**
\[
f(2x - 3) = 3(2x - 3) + 4
\]
**Step 4: Simplify the Expression**
\[
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
\]
**Final Answer:**
\[
f \circ g(x) = 6x - 5
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). Starting with \( g(x) = 2x - 3 \), we will replace \( x \) in \( f(x) = 3x + 4 \) with \( g(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] Now, substitute \( 2x - 3 \) into \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, \[ f \circ g(x) = 6x - 5 \]
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