Question
Using the following equations, find \( f(g(x)) \) : \( f(x)=-2 x+5 \) \( g(x)=3 x-9 \) \( f(g(x))=[?] x+\square \)
Ask by Little Bryant. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(g(x)) = -6x + 23 \)
Solution
To find \( f(g(x)) \), we'll substitute \( g(x) \) into \( f(x) \).
Given:
- \( f(x) = -2x + 5 \)
- \( g(x) = 3x - 9 \)
**Step 1:** Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(3x - 9)
\]
**Step 2:** Apply the function \( f \) to \( 3x - 9 \):
\[
f(3x - 9) = -2(3x - 9) + 5
\]
**Step 3:** Distribute and simplify:
\[
-2(3x) + (-2)(-9) + 5 = -6x + 18 + 5 = -6x + 23
\]
So,
\[
f(g(x)) = -6x + 23
\]
**Final Answer:**
\[
f(g(x)) = -6x + 23
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find \( f(g(x)) \), we start by substituting \( g(x) \) into \( f(x) \). First, we find \( g(x) \): \[ g(x) = 3x - 9 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(3x - 9) = -2(3x - 9) + 5 \] Now, distribute the \(-2\): \[ = -6x + 18 + 5 \] \[ = -6x + 23 \] So, we have: \[ f(g(x)) = -6 x + 23 \] Thus, the final answer is: \[ f(g(x)) = -6 x + 23 \]
