Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Johnson Graham. in South Africa
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
f ∘ g(x) = 6x – 5
Solution
To find f ∘ g(x), substitute g(x) into f(x).
Step 1: Write down g(x):
g(x) = 2x – 3
Step 2: Substitute g(x) into f(x):
f(g(x)) = 3(g(x)) + 4 = 3(2x – 3) + 4
Step 3: Simplify:
= 6x – 9 + 4
= 6x – 5
Thus, f ∘ g(x) = 6x – 5.
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Simplify this solution Mind Expander
To find \( f \circ g(x) \), we need to compose the functions \( f(x) \) and \( g(x) \). This means we will substitute \( g(x) \) into \( f(x) \). First, we find \( g(x) \): \[ g(x) = 2x - 3 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, we replace \( x \) in \( f(x) = 3x + 4 \) with \( 2x - 3 \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, distribute the 3: \[ = 6x - 9 + 4 \] Finally, combine like terms: \[ = 6x - 5 \] So, the result of \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]
