Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Page Kelly. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
To find f ∘ g(x), substitute g(x) into f(x):
1. Given f(x) = 3x + 4 and g(x) = 2x – 3.
2. Compute f(g(x)) = f(2x – 3) = 3(2x – 3) + 4.
3. Distribute and simplify: 3(2x – 3) = 6x – 9.
4. Then add 4: 6x – 9 + 4 = 6x – 5.
Thus, f ∘ g(x) = 6x – 5.
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Simplify this solution The Deep Dive
To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now substitute \( 2x - 3 \) into the formula for \( f(x) \): \[ f(x) = 3x + 4 \] Thus: \[ f(2x - 3) = 3(2x - 3) + 4 \] Distributing the \( 3 \): \[ = 6x - 9 + 4 \] Combining the constants: \[ = 6x - 5 \] So, the final result for \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]
