Question

for f(x) = x+1 and g(x)= 2x+3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.(gof)(2)

Answer 1

Answer:

a)  2x + 4

b)  2x + 5

c)  8

d)  9

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}$

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)

$\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}$

Part (b)

$\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}$

Part (c)

$\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}$

Part (d)

$\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}$

Learn more about composite functions here:

https://brainly.com/question/27966754

https://brainly.com/question/28062427

Answer 2

• f(x)=x+1
• g(x)=2x+3

(fog)(x)

• f(g(x))
• f(2x+3)
• 2x+3+1
• 2x+4

(gof)(x)

• g(f(x))
• g(x+1)
• 2x+2+3
• 2x+5

(fog)(2))

• 2(2)+4
• 8

(gof)(2)

• 2(2)+5
• 9