Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Ford Potter. in South Africa
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
To find \( f \circ g(x) \), we need to substitute the expression for \( g(x) \) into the expression for \( f(x) \).
Given:
\[ f(x) = 3x + 4 \]
\[ g(x) = 2x - 3 \]
Substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = 3(2x - 3) + 4 \]
Now, simplify the expression:
\[ f(g(x)) = 6x - 9 + 4 \]
\[ f(g(x)) = 6x - 5 \]
Therefore, \( f \circ g(x) = 6x - 5 \).
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Simplify this solution Beyond the Answer
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). This means we will take \( g(x) = 2x - 3 \) and plug it into \( f(x) \): \[ f(g(x)) = f(2x - 3) = 3(2x - 3) + 4 \] Now, let's simplify this: \[ f(g(x)) = 3 \cdot 2x - 3 \cdot 3 + 4 = 6x - 9 + 4 = 6x - 5 \] Therefore, the result is: \[ f \circ g(x) = 6x - 5 \]
