Evaluating Composite Functions given the Table of Values
Answer:
[tex]f(g(4)) = -4[/tex]
Step-by-step explanation:
Given:
[tex]&x &-3 &-2 &-1 &4 &6 &9 \\ &f(x) &2 &4 &9 &1 &-4 &-2 \\ &g(x) &-6 &1 &4 &6 &9 &3[/tex]
Before we can solve for [tex]f(g(4))[/tex], we can solve for [tex]g(4)[/tex] first. [tex]g(4)[/tex] means that it is the value of [tex]g(x)[/tex] when [tex]x = 4[/tex]. We can see that when [tex]x = 4[/tex], the table tells us that [tex]g(x) = 6[/tex].[tex]g(4) = 6[/tex].
Now we have solved for [tex]g(4)[/tex], we can now solve for [tex]f(g(4))[/tex]. Since [tex]g(4) = 6[/tex], [tex]f(g(4)) = f(6)[/tex]. Finding the value [tex]f(6)[/tex] is just the same process as finding the value of [tex]g(4)[/tex]. When [tex]x = 6[/tex], [tex]f(x) = -4[/tex]. This means that [tex]f(6) = -4[/tex].
So [tex]f(g(4)) = -4[/tex].
To know more about Composite Functions, you can see my Answers from these Questions:
- brainly.com/question/24614010
- brainly.com/question/24619506
