High School

We appreciate your visit to Let ℤ denote the set of positive integers When tex f x x 2 1 tex let tex g tex be the function defined by. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Let ℤ⁺ denote the set of positive integers. When [tex]f(x) = x^2 + 1[/tex], let [tex]g[/tex] be the function defined by [tex]g(x) = f(f(x))[/tex]. What is [tex]g(3)[/tex]?

A. 11
B. 27
C. 37
D. 83

Answer :

Final Answer:

The value of ( g(3) ) is 101. Option c) 101 is the correct choice.

Explanation:

1. Find ( f(3) ):

  • Given [tex]\( f(x) = x^2 + 1 \),[/tex] plug in ( x = 3 ) to find ( f(3) ).
  • [tex]\( f(3) = 3^2 + 1 = 9 + 1 = 10 \).[/tex]

2. Find ( g(3) ):

  • Since [tex]\( g(x) = f(f(x)) \),[/tex] we need to find ( f(10) ) to determine ( g(3) ).
  • Substitute ( x = 10 ) into the function [tex]\( f(x) = x^2 + 1 \)[/tex] to find ( f(10) ).
  • [tex]\( f(10) = 10^2 + 1 = 100 + 1 = 101 \).[/tex]

By following these steps, we determine that ( g(3) ) is indeed 101. This process highlights the importance of understanding function composition and applying it correctly to find the value of a composite function. Through clear calculation and substitution, we derive the correct value of ( g(3) ) as 101, reinforcing the importance of systematic problem-solving techniques in mathematics. Therefore, option c) 101 is the correct choice.

Question

Let ℤ+ denote the set of positive integers. When f(x) = x² + 1, let g be the function defined by g(x) = f(f(x)). What is g(3)?

a) 11

b) 27

c) 101

d) 83

Thanks for taking the time to read Let ℤ denote the set of positive integers When tex f x x 2 1 tex let tex g tex be the function defined by. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada