Answer:
a) 2x + 4
b) 2x + 5
c) 8
d) 9
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]
Function composition is an operation that takes two or more functions and combines them into a single function.
(f o g)(x) means find g(x) first and then substitute the result into f(x).
(g o f)(x) means find f(x) first and then substitute the result into g(x).
Part (a)
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]
Part (d)
[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]
Learn more about composite functions here:
https://brainly.com/question/27966754
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