Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Vega Potter. in Nigeria
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. We are given the functions:
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3.
\]
2. The composition \( f \circ g(x) \) means:
\[
f(g(x)).
\]
3. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3).
\]
4. Replace the variable in \( f(x) \) with \( 2x - 3 \):
\[
f(2x - 3) = 3(2x - 3) + 4.
\]
5. Distribute and simplify:
\[
3(2x - 3) = 6x - 9.
\]
Therefore,
\[
6x - 9 + 4 = 6x - 5.
\]
6. The final result is:
\[
f \circ g(x) = 6x - 5.
\]
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Simplify this solution Mind Expander
To find \( f \circ g(x) \), you substitute \( g(x) \) into \( f(x) \). Start with: \[ g(x) = 2x - 3 \] Now, replace \( x \) in \( f(x) = 3x + 4 \) with \( g(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Distributing the 3: \[ = 6x - 9 + 4 \] Combine like terms: \[ = 6x - 5 \] Thus, \( f \circ g(x) = 6x - 5 \).
