Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Simpson Norton. in Australia
Mar 20,2025
Solución de inteligencia artificial de Upstudy
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\( f \circ g(x) = 6x - 5 \)
Solución
1. We are given the functions
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3.
\]
2. The composite function \( f \circ g(x) \) is defined as
\[
f \circ g(x) = f(g(x)).
\]
3. Substitute \( g(x) = 2x - 3 \) into \( f(x) \):
\[
f(g(x)) = 3(2x - 3) + 4.
\]
4. Distribute and simplify:
\[
3(2x - 3) + 4 = 6x - 9 + 4.
\]
\[
6x - 9 + 4 = 6x - 5.
\]
5. Therefore, the composite function is:
\[
f \circ g(x) = 6x - 5.
\]
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Simplifique esta solución Extra Insights
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we have: \[ g(x) = 2x - 3 \] Now substitute \( g(x) \) into \( f(x) \): \[ f \circ g(x) = f(g(x)) = f(2x - 3) \] Next, we plug \( 2x - 3 \) into \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, distribute the 3: \[ = 6x - 9 + 4 \] Then combine like terms: \[ = 6x - 5 \] So, the result is: \[ f \circ g(x) = 6x - 5 \]
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