Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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)

Sagot :

semsee45

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

https://brainly.com/question/28062427

MisterBrainly
  • 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
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.