Question
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Ask by Kelly Barker. in South Africa
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f \circ g(x) = 6x - 5 \)
Solution
1. Write the composition \( f \circ g(x) = f(g(x)) \).
2. Substitute \( g(x) = 2x-3 \) into \( f(x)=3x+4 \):
\[
f(g(x)) = 3(2x-3) + 4
\]
3. Distribute the \( 3 \):
\[
f(g(x)) = 6x - 9 + 4
\]
4. Combine like terms:
\[
f(g(x)) = 6x - 5
\]
Thus,
\[
f \circ g(x)=6x-5.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the composition \( f \circ g(x) \), we will substitute \( g(x) \) into \( f(x) \). This means we will replace every instance of \( x \) in \( f(x) \) with \( g(x) \). 1. We start with the functions: \[ f(x) = 3x + 4 \] \[ g(x) = 2x - 3 \] 2. Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] 3. Next, replace \( x \) in \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] 4. Simplify it: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the final result is: \[ f \circ g(x) = 6x - 5 \]
