Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Norris Gibbs. in South Africa
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. Start with the functions:
\[
f(x) = 3x + 4, \quad g(x) = 2x - 3
\]
2. Find the composition \( f \circ g(x) \) by substituting \( g(x) \) into \( f \):
\[
f(g(x)) = 3(2x - 3) + 4
\]
3. Distribute and simplify:
\[
f(g(x)) = 6x - 9 + 4 = 6x - 5
\]
Thus, the composition is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution Mind Expander
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). Start by computing \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify the expression: \[ = 3 \cdot 2x - 3 \cdot 3 + 4 \] \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, \( f \circ g(x) = 6x - 5 \).
