Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Norton Ross. in the United States
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 a composition of functions:
\[
(f \circ g)(x) = f(g(x))
\]
2. Substitute \( g(x) = 2x - 3 \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3)
\]
3. The function \( f(x) \) is given by \( f(x) = 3x + 4 \). Replace \( x \) with \( 2x - 3 \) in this expression:
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. Distribute the 3:
\[
3(2x - 3) = 6x - 9
\]
5. Add the 4:
\[
6x - 9 + 4 = 6x - 5
\]
6. Therefore, the composition \( f \circ g(x) \) is:
\[
(f \circ g)(x) = 6x - 5
\]
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Simplifique esta solución Mind Expander
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). 1. First, we calculate \( g(x) \): \[ g(x) = 2x - 3 \] 2. Next, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] 3. Now, apply the function \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] 4. Distributing the \( 3 \): \[ = 6x - 9 + 4 \] 5. Simplify it: \[ = 6x - 5 \] Thus, the final result is: \[ f \circ g(x) = 6x - 5 \]
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