Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Estrada Ramirez. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
To find the composition \( f \circ g(x) \), we substitute \( g(x) \) into \( f(x) \).
Given:
\[
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
\]
Compute \( f(g(x)) \):
\[
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
\]
\[
= 6x - 9 + 4
\]
\[
= 6x - 5
\]
So, the composition \( f \circ g(x) \) is:
\[
f \circ g(x) = 6x - 5
\]
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Simplify this solution The Deep Dive
To find \( f \circ g(x) \), which means \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). First, let's calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, using the function \( f(x) = 3x + 4 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing the 3: \[ = 6x - 9 + 4 \] Combining the constants: \[ = 6x - 5 \] Thus, the result of \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]
