Question

Algebra Use the pair of functions to find

f(g(x)) and g(f(x)).
Simplify your answers.
f(x) = x2 + 9, g(x) = Square root x + 6


f(g(x)) =
g(f(x)) =

Answer 1

Hey miss Emily c:

\[\large\rm f=x^2+9\qquad\qquad\qquad g=\sqrt{x+6}\]
So for this first one,\[\large\rm f(g)\]they want us to take all of g,
and stick it place of the x in our f function,\[\large\rm f(g)=g^2+9\]See how I replaced the x with g?
Ok but g is actually sqrt(x+6), so let's write our g that way,\[\large\rm f(g)=(\sqrt{x+6})^2+9\]

Answer 2

simplify from that point.

Answer 3

How do i simplify?

Answer 4

square root and square are `opposite` or `inverse` operations of one another.
So they "undo" one another.\[\large\rm (\sqrt{x+6})^2\quad=\quad x+6\]See how the square root and the square both disappear?
Ya, they were able to undo one another.

So that would be the first step in simplifying.
Next combine any like-terms.

Answer 5

\[g(x)=x+5\] what is \(g(5)\)?

Answer 6

x?

Answer 7

lol

Answer 8

\[g(x)=x+5\\
g(5)=5+5=?\]

Answer 9

10? idk

Answer 10

don't laugh at me lol

Answer 11

yes, 5+5=10

Answer 12

now \[f(x)=2x+3\]so \(f(10)=?\)

Answer 13

20?

Answer 14

no, \(2\times 10=20\) you need \(2\times 10+3=20+3=?\)

Answer 15

23

Answer 16

im lost

Answer 17

whew
that is your answer to the first one

Answer 18

ahahaha "whew" see what i mean? its impossible.

Answer 19

no you aren't lost \[f(g(5))=f(1)=23\] so \(23\) is the answer

Answer 20

ok typo there \[f(g(5))=f(10)=23\]

Answer 21

get out the calculator for the next one
ready?

Answer 22

okay

Answer 23

\[C(s(h))=C(25h)=45\times 25h+560\] you have to compute \(45\times 25\)

Answer 24

so 45 times 25?

Answer 25

1125

Answer 26

i believe you
put \(1125h+560\) in the first box

Answer 27

then for the second part, \(h=6\) use your calculator to compute \[1125\times 6+560\]

Answer 28

7310

Answer 29

ok next question

Answer 30

yes 7310

Answer 31

this a repeat?

Answer 32

no question we haven't done yet

Answer 33

you put \(x=9\) get \[9^3-2-\frac{9}{9-10}\]

Answer 34

\[f(3)=3^2-3\times 3-4=?\]

Answer 35

12

Answer 36

no actually \[9-9-4\neq 12\]

Answer 37

nice and slow for this one
what is \(g(3)\)? if it is not clear, say so

Answer 38

is that like 3 x 3

Answer 39

no, \(g\) is a set of ordered pairs, things that look like \((a,b)\)
find the ordered pair in the list where the first number is 3, i.e. \((3,?)\) what is the second number?

Answer 40

idk

Answer 41

oh dear, look with your eyes, there is nothing to compute here. where do you see a pair that starts with the number 3?

Answer 42

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