Question

Helppp

Answer 1

so the function notation f(a) means "the value of the function f when a is substituted into the equation for x"

Answer 2

so f(2) means "the value of the function f when 2 is substituted into the equation for x"

Answer 3

so to find f(2) replace "x" with 2 and find f(x) = 3x^2 + 2x + 4

Answer 4

20

Answer 5

good!

now we replace "x" with "a+h" and find f(x) = 3x^2 + 2x + 4

your answer will not be a number, it will be a polynomial with a and h

Answer 6

wait I got.. \[3a^2+3h^2+2a+2h+4\]

Answer 7

be careful

(a+h)^2 is not a^2 + h^2 (this is a really common mistake though)

Answer 8

(a+h)^2 = (a+h)(a+h) = ?

use foil to expand this

Answer 9

what am I solving for again a or h?

Answer 10

you are not solving for a or h

Answer 11

f(a+h) just means, find f(x) when x = a + h

therefore we are just plugging in "a+h" into f(x) and simplifying

Answer 12

3x^2 + 2x + 4 = 3(a+h)^2 + 2(a+h) + 4 = ?

Answer 13

\[3a^2+6ah+3h^2+2a+2h+4\]

Answer 14

awesome, that's the answer

Answer 15

Great !!! Now for #12

Answer 16

f○g = f(g(x))

to find f○g(2) we simply find g(2), take the result of that, and find f(x) of that value

Answer 17

so g(2) = ?

Answer 18

17

Answer 19

good and f(17) = ?

Answer 20

sorry I was afk

Answer 21

\[\frac{ 1 }{ 17 }\]

Answer 22

good so that's the ans to f○g(2)

Answer 23

to find (f+g)(2) just add f(x) and g(x) together then let x = 2

Answer 24

17.5

Answer 25

good that's it for 12

Answer 26

for 13 we use a similar process to 12 but we use the table instead of an equation

Answer 27

g(1) = ?

Answer 28

6

Answer 29

good and f(6) = ?

Answer 30

17

Answer 31

good that's it for 13

Answer 32

so just 6 and 17

Answer 33

the answer is 17 not 6

Answer 34

oh because g(1) is 6

Answer 35

yes

Answer 36

so the final answer is 17

Answer 37

yes