Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Owen Lee. in Ghana
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
f ∘ g(x) = 6x - 5
Solution
To find f ∘ g(x), we start by substituting the function g(x) into the function f(x).
Step 1: Write the functions:
f(x) = 3x + 4
g(x) = 2x - 3
Step 2: Substitute g(x) into f(x):
f(g(x)) = 3*(g(x)) + 4
= 3*(2x - 3) + 4
= 6x - 9 + 4
Step 3: Simplify:
f(g(x)) = 6x - 5
So, the composition f ∘ g(x) = 6x - 5.
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Simplify this solution Extra Insights
To find \( f \circ g(x) \), which means \( f(g(x)) \), we first need to plug \( g(x) \) into \( f(x) \). Given: \[ g(x) = 2x - 3 \] Now substituting \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, we substitute \( 2x - 3 \) into the formula for \( f(x) \): \[ f(x) = 3x + 4 \quad \Rightarrow \quad f(2x - 3) = 3(2x - 3) + 4 \] Now, perform the multiplication: \[ = 6x - 9 + 4 \] Simplifying it gives: \[ = 6x - 5 \] Thus, the result of \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]
