Question

Use the Table to evaluate each expression.

x | 1 2 3 4 5 6
f | 3 1 4 2 2 5
g | 6 3 2 1 2 3

a). f(g(1))
b). g(f(1))
c). f(f(1))
d). g(g(1))
e). (gof)(3)
f). (fog)(6)

help me understand the concept and how to do it, and I'll try on my own

Answer 1

following your table u got
\[ \large f(g(1))=f(6)=5 \]
got it???

Answer 2

nope.. I need like step by step instructions.. ?

Answer 3

g(1) means value of g at x=1

Answer 4

ok. but u do understand the table, don't u???

Answer 5

I don't know how to use the table to find the answer. That's my issue.

Answer 6

now g at x=1 is 6 ...therefore now F(6) is the value of f at x=6 which is 5

Answer 7

the first line gives u the value of the independent variable: 1 through 6
the second line tells u that the function \(f\) transforms 1 into 3 hence f(1)=3
got it??

Answer 8

okay, so for the second one.. x=1 f(3) g(2).. so 2 is the answer?

Answer 9

yes

Answer 10

and the third is 3?

Answer 11

\[ \large g(f(1))=g(3)=2 \]

Answer 12

try writing it the way i did!!!

Answer 13

no, the third is not 3

Answer 14

oh four?

Answer 15

f(f(1))=f(3)=4

Answer 16

yes. u got it!!

Answer 17

g(g(1))=g(6)=3?

Answer 18

yes

Answer 19

\[ \large (g\circ f)(3)=g(f(3))= \]

Answer 20

how do I solve the last two cause they're differentt...

Answer 21

is (gof)(3)=1?
(fog)(6)=4?

Answer 22

yes to both!!
did u understand???

Answer 23

yeah thank you :)

Answer 24

u r welcome