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are you able to determine f(g(x)) ?

I have trouble with it.

maybe we can write it differently like instead of f(g(x)) we can write f o g

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and for g(f(x)) -> g o f

I had to read these questions from right to left when I first did them

Kinda, yes

what does 2(5x+1) - 6 simplify to?

Distribute the 2 in the parenthesis?

yes, then what?

distribute the 2 for (5x+1) and then combine like terms

Is it possible to multiply 5x by 2?

yes you will multiply the outer 2 by each term inside

distribution is multiplication
so multiply 2 times 5x and 2 x 1

|dw:1434845209689:dw|

(10x + 2)-6

you can toss those parenthesis since they aren't needed

correct
10x+2-6
so now we need 2-6

-4

\[2(5x+1)-6 \rightarrow 10x+2-6 \rightarrow 10x-4\]

yes so that's our f(g(x)) or f o g
10x - 4

How do I translate that to the answer choices.

are you able to use these steps to figure out g(f(x)) ?

can't wait to see the answer to ", which composition produces the greatest output?"

blame the publishers.

I'm really confused.

you ought to be !

How do I set up g(f(x))?

recall that our functions are f(x) = 2x-6 and g(x) = 5x+1

5(2x-6)+1 ?

then on the right side, replace f(x) with 2x-6
so yeah you have it, 5(2x-6) + 1

O_O unheard that's right... now we need to distribute and simplify

simplify 5(2x-6) + 1

what is 5 times 2x
and what is 5 x -6 ?

10x+30+1

you have a sign error

5 multiplied by -6 = ?

Oops, yeah, I dont have my glasses on. One sec.

-30

yes
\[10x-30+1\]

so now what is -30+1 ?

-29

mhm \[10x-29\] is our g(f(x))
and \[10x-4 \] is our f(g(x))

So how does that translate to my answer choices.

Which is more?

Let's say x = 0.
What is f(g(x)) equal to?
What is g(f(x)) equal to?

10x-4
10x+-29

in each case, replace x with 0 and compute

subsitute x = 0 into both equations

0-4
0+-29

ok so what's 0-4 and 0-29?

4
29

uhhhhh... no... that's positive numbers... we are dealing with negative numbers

think of it as ... you are charged $4 but don't have any money ... you have a negative balance

-4
-29

yes
:)

now... bigger negative numbers are much smaller in value than single digit negative numbers

so, f(g(x))!!

yeah... -4 is bigger than -29

Thank you.

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