Question
f(x) = 3x + 4 quad g(x) = 2x - 3 Find: f ∘ g(x)
Ask by Griffiths Wagner.
Feb 23,2025 18:02
UpStudy AI Solution
Tutor-Verified Answer
Answer
(f ∘ g)(x) = 6x - 5
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
To find \( f \circ g(x) \), we will substitute \( g(x) \) into \( f(x) \).
First, we calculate \( g(x) \):
\[
g(x) = 2x - 3
\]
Now, we will substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(2x - 3)
\]
Next, we plug \( 2x - 3 \) into the function \( f(x) = 3x + 4 \):
\[
f(2x - 3) = 3(2x - 3) + 4
\]
Now, simplify this:
\[
= 6x - 9 + 4
\]
\[
= 6x - 5
\]
Thus, the result of \( f \circ g(x) \) is:
\[
f \circ g(x) = 6x - 5
\]
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