Discover the best answers to your questions with the help of IDNLearn.com. Discover comprehensive answers to your questions from our community of knowledgeable experts.
Sagot :
Given the function [tex]\( f(x) \)[/tex] provided in the table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -6 & 1 \\ \hline -3 & 2 \\ \hline 2 & 5 \\ \hline 5 & 3 \\ \hline 8 & 0 \\ \hline \end{array} \][/tex]
We need to find [tex]\( f(g(2)) \)[/tex], where [tex]\( g(x) \)[/tex] is the inverse function of [tex]\( f(x) \)[/tex].
1. First, recognize that [tex]\( g(x) \)[/tex] being the inverse of [tex]\( f(x) \)[/tex] means that [tex]\( g \)[/tex] swaps the roles of the inputs and outputs of [tex]\( f \)[/tex]. In other words, if [tex]\( f(a) = b \)[/tex], then [tex]\( g(b) = a \)[/tex].
2. Identify [tex]\( g(2) \)[/tex]:
- Look in the table to see which [tex]\( x \)[/tex] value corresponds to [tex]\( f(x) = 2 \)[/tex].
- From the table: [tex]\( f(-3) = 2 \)[/tex].
Thus, [tex]\( g(2) = -3 \)[/tex].
3. Now, evaluate [tex]\( f(g(2)) \)[/tex]:
- Substitute [tex]\( g(2) \)[/tex] into [tex]\( f \)[/tex], which is [tex]\( f(-3) \)[/tex].
- From the table, we know that [tex]\( f(-3) = 2 \)[/tex].
Therefore, the value of [tex]\( f(g(2)) \)[/tex] is [tex]\( 2 \)[/tex].
[tex]\[ \boxed{2} \][/tex]
So the correct answer is 2.
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -6 & 1 \\ \hline -3 & 2 \\ \hline 2 & 5 \\ \hline 5 & 3 \\ \hline 8 & 0 \\ \hline \end{array} \][/tex]
We need to find [tex]\( f(g(2)) \)[/tex], where [tex]\( g(x) \)[/tex] is the inverse function of [tex]\( f(x) \)[/tex].
1. First, recognize that [tex]\( g(x) \)[/tex] being the inverse of [tex]\( f(x) \)[/tex] means that [tex]\( g \)[/tex] swaps the roles of the inputs and outputs of [tex]\( f \)[/tex]. In other words, if [tex]\( f(a) = b \)[/tex], then [tex]\( g(b) = a \)[/tex].
2. Identify [tex]\( g(2) \)[/tex]:
- Look in the table to see which [tex]\( x \)[/tex] value corresponds to [tex]\( f(x) = 2 \)[/tex].
- From the table: [tex]\( f(-3) = 2 \)[/tex].
Thus, [tex]\( g(2) = -3 \)[/tex].
3. Now, evaluate [tex]\( f(g(2)) \)[/tex]:
- Substitute [tex]\( g(2) \)[/tex] into [tex]\( f \)[/tex], which is [tex]\( f(-3) \)[/tex].
- From the table, we know that [tex]\( f(-3) = 2 \)[/tex].
Therefore, the value of [tex]\( f(g(2)) \)[/tex] is [tex]\( 2 \)[/tex].
[tex]\[ \boxed{2} \][/tex]
So the correct answer is 2.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.