Question

Complete the table given that h(x) = f(g(x))
x f(x) g(x) h(x)
0 1 2 3
1 9 0 1
2 ? 1 9

Answer 1

the missing value will be f(2)

that value is on the table somewhere already

Answer 2

so would it be 0?

Answer 3

h(x) = f [ g(x) ]

compound function, x--->g(x)--->f(x) ------>h(x)


starting with a value for x

you can get g(x), then f(x) is evaluated at that value for g(x)

do you understand the nested function thing?

Answer 4

yes

Answer 5

look at row 2

x=1, g(1) = 0, f(g(1)) = f(0) = 1 [from row 1 when x=0]

Answer 6

notice that matches h(1)

Answer 7

to figure f(x) when x is 2

need to find where g(x) = 2, and use that value in f(x)

Answer 8

g(x) = 2 when x=0

Answer 9

yea so do you plug in 0 in f(x) now?

Answer 10

f(0) is 1,

Answer 11

huh ok that makes some sense now thank you!

Answer 12

h(2) = 9

f [ g(2)] = f [ 1] = 9

Answer 13

im sorry, but im lost again, how does finding that help get f(2)?

Answer 14

k...


th emissing value is f(x) at x=2

Answer 15

but f(x) is defined in terms of g(x)

Answer 16

so to get f(2), you need g(x) = 2

Answer 17

which is 0?

Answer 18

and then what would you do?

Answer 19

i need sleep.. lol here

Answer 20

ahhh np man go ahead

Answer 21

need f(x) = f(2), x=2

Answer 22

f[ g[x]]

start with x=2
g(2) = 1

f[g(2)] = f[1] = 9


so f(2) = 9

Answer 23

which should be h(2), good both are 9

Answer 24

well alright then, thank you and have a good night!

Answer 25

welcome, sorry took so long

Answer 26

want f when x=2

figure h(2) = 1 h(x) = 1 when x=2

Answer 27

so f(g(2)) = f(1)

f(1) = 9 when x=1

Answer 28

so f(2) = 9

Answer 29

alright thanks!