Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Powell Sandoval. in Nigeria
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
Simplify the expression by following steps:
- step0: Multiply the terms:
\(f\left(gx\right)\)
- step1: Multiply the terms:
\(fgx\)
Substitute \( x=2x-3 \) into the expression \( 3(2x - 3) + 4 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(3\left(2x-3\right)+4\)
- step1: Substitute:
\(3\left(2\left(2x-3\right)-3\right)+4\)
- step2: Subtract the terms:
\(3\left(4x-9\right)+4\)
- step3: Expand the expression:
\(12x-27+4\)
- step4: Add the numbers:
\(12x-23\)
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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Simplify this solution Mind Expander
To find \( f \circ g(x) \), you need to substitute \( g(x) \) into \( f(x) \). First, compute \( g(x) \): \[ g(x) = 2x - 3 \] Now substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now simplify: \[ = 6x - 9 + 4 = 6x - 5 \] Therefore, \( f \circ g(x) = 6x - 5 \).
