Here we have a problem of composition of functions.
Remember that:
(f ° g)(x) = f( g(x) )
Now we have the table:
x | 1 2 3 4 5 6
f(x) | 6 4 4 1 6 4
g(x) | 5 5 2 1 4 3
Using the table, we want to find:
To read the table, for example for f(5) first you go to the "x" part of the table and find the 5.
Now you go to the f(x) table and see which is the value of f(5), in this case, we can see that f(5) = 6.
a) f(g(1))
First, looking at the table, we can see that:
g(1) = 5
Then:
f(g(1)) = f(5)
Again, looking at the table we can see that f(5) = 6
Then we have:
f(g(1)) = 6
b) g(f(1))
Same approach as before:
f(1) = 6
then g(f(1)) = g(6)
And looking at the table, g(6) = 3
Then: g(f(1)) = 3
c) f(f(1))
f(1) = 6
f(f(1)) = f(6) = 4
f(f(1)) = 4
d) g(g(1))
g(1) = 5
then:
g(g(1)) = g(5) = 4
g(g(1)) = 4
e) (gof)(3)
This is equal to:
(gof)(3) = g(f(3))
we know that f(3) = 4
then:
g(f(3)) = g(4) = 1
(gof)(3) = 1
f) (fog)(6) = f(g(6))
We can see that:
g(6) = 3
then:
f(g(6)) = f(3) = 4
Concluding:
(fog)(6) = 4
If you want to learn more, you can read:
https://brainly.com/question/8308119
