Pregunta
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Bright Smith. in Nigeria
Feb 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( f \circ g(x) = 6x - 5 \)
Solución
Simplify the expression by following steps:
- step0: Multiply the terms:
\(f\left(gx\right)\)
- step1: Multiply the terms:
\(fgx\)
Expand the expression \( 3(2x - 3) + 4 \)
Simplify the expression by following steps:
- step0: Add the terms:
\(3\left(2x-3\right)+4\)
- step1: Expand the expression:
\(6x-9+4\)
- step2: Add the numbers:
\(6x-5\)
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \).
1. **Identify the functions:**
- \( f(x) = 3x + 4 \)
- \( g(x) = 2x - 3 \)
2. **Substitute \( g(x) \) into \( f(x) \):**
\[
f(g(x)) = f(2x - 3)
\]
3. **Calculate \( f(2x - 3) \):**
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. **Expand the expression:**
\[
= 6x - 9 + 4
\]
\[
= 6x - 5
\]
Thus, the result of \( f \circ g(x) \) is:
\[
f \circ g(x) = 6x - 5
\]
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Simplifique esta solución The Deep Dive
To find \( f \circ g(x) \), which represents the composition of the functions \( f \) and \( g \), we need to substitute \( g(x) \) into \( f(x) \). First, we calculate \( g(x) \): \[ g(x) = 2x - 3 \] Next, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, we replace \( x \) in \( f(x) = 3x + 4 \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, the result is: \[ f \circ g(x) = 6x - 5 \]
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