Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Perkins Washington. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. Write the definition of the compound function \( f \circ g \):
\[
f \circ g (x) = f(g(x))
\]
2. Substitute the definition of \( g(x) \) into \( f(x) \). Given:
\[
g(x) = 2x - 3, \quad f(x) = 3x + 4
\]
we have:
\[
f(g(x)) = 3(2x - 3) + 4
\]
3. Distribute and simplify:
\[
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
\]
4. Therefore, the composite function is:
\[
f \circ g (x) = 6x - 5
\]
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Simplify this solution Mind Expander
To find \( f \circ g(x) \), we will substitute \( g(x) \) into \( f(x) \). First, we define \( g(x) \): \[ g(x) = 2x - 3 \] Now, we will substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, we use the function \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, \( f \circ g(x) = 6x - 5 \).
