Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Vaughan George. in Italy
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 \( f \circ g(x) \), we need to apply function \( g \) first and then apply function \( f \) to the result of \( g(x) \).
Given:
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
\]
**Step 1: Compute \( g(x) \)**
First, apply the function \( g \) to \( x \):
\[
g(x) = 2x - 3
\]
**Step 2: Compute \( f(g(x)) \)**
Next, apply the function \( f \) to the result of \( g(x) \):
\[
f(g(x)) = f(2x - 3)
\]
Substitute \( 2x - 3 \) into \( f(x) \):
\[
f(2x - 3) = 3(2x - 3) + 4
\]
**Step 3: Simplify the Expression**
Now, distribute and simplify:
\[
f(2x - 3) = 3 \cdot 2x - 3 \cdot 3 + 4 = 6x - 9 + 4
\]
\[
f(2x - 3) = 6x - 5
\]
**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 Bonus Knowledge
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, distribute and simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] So, \( f \circ g(x) = 6x - 5 \).
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