Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Chadwick Wilson. in China
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. Write the expression for \( f \circ g(x) \):
\[
f \circ g(x) = f(g(x))
\]
2. Substitute \( g(x) = 2x - 3 \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3)
\]
3. Replace \( x \) with \( 2x - 3 \) in the formula for \( f(x) \):
\[
f(2x - 3) = 3(2x - 3) + 4
\]
4. Distribute and simplify:
\[
3(2x - 3) = 6x - 9
\]
\[
6x - 9 + 4 = 6x - 5
\]
5. The final answer is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution Bonus Knowledge
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). Given: \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify this: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, \[ f \circ g(x) = 6x - 5 \]
