Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Lyons Graham. in Germany
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
f ∘ g(x) = 6x - 5
Solution
To find the composite function f ∘ g(x), substitute g(x) into f(x):
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
Now, distribute and simplify:
= 6x - 9 + 4
= 6x - 5
Thus, f ∘ 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 \( f(x) \). First, calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Now, using the definition of \( f(x) \): \[ f(x) = 3x + 4 \] we plug \( 2x - 3 \) into \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify this expression: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] So, the final answer is: \[ f \circ g(x) = 6x - 5 \]
