Question

f(x)= 2x+3 g(x) = 5 - 4x x=4
Solve for f(g(x)) and g(f(x))

Answer 1

\[\Large f(x)=2x+3 \qquad \qquad g(x)= 5-4x\qquad\qquad x=4\]
Hmm I'm trying to figure out why they included x=4.
They probably meant that they want us to solve for,
\(\large f(g(4)) \qquad\text{and}\qquad g(f(4))\)

Answer 2

\[\Large f(\color{royalblue}{x})=2\color{royalblue}{x}+3\]For the first one, we want to plug g(x) in for our blue x that's in f.\[\Large f(\color{royalblue}{g(x)})=2\color{royalblue}{g(x)}+3\]Which gives us,\[\Large f(\color{royalblue}{g(x)})=2\color{royalblue}{(5-4x)}+3\]

Answer 3

If we wanted to evaluate this at x=4, we have,\[\Large f(\color{royalblue}{g(4)})=2\color{royalblue}{(5-4\cdot4)}+3\]

Answer 4

What do you think Crys? :x too confusing?

Answer 5

No I get the concept! :)

Answer 6

Will the answer be 11? @zepdrix

Answer 7

For f(g(4))? Hmm it looks like it's -19.

\[\Large f(4)=2\cdot4+3=11\]
Did you calculate that out by mistake? :o

Answer 8

yea i used calculator

Answer 9

\[\Large \color{royalblue}{g(4)=5-4\cdot4=-11}\]\[\Large \color{royalblue}{g(4)=-11}\]
We want to plug this value in for f(x).

Answer 10

\[\Large f(\color{royalblue}{g(4)}) \qquad=\qquad f(\color{royalblue}{-11})\]

Answer 11

\[\Large f(-11)=2(-11)+3\]

Answer 12

Ok I see how I get -19 now!

Answer 13

Function notation so confusing! :) Takes a little getting used to.
Try to find your g(f(4)) also

Answer 14

I just did pemdas

Answer 15

Ok Ill let u know what I get

Answer 16

So will it start out with 5-4x(2x+3)

Answer 17

5-4(2x+3)

careful, i see an extra x in there! :O
we `replace` the x with that big mess of parentheses.

Answer 18

how is that?

Answer 19

ohhhh i seee lol

Answer 20

distrubuted and got 10x +15 -8x-12

Answer 21

do i sub the 4 now?

Answer 22

oh sorry i disappeared there +_+
Hmmm i don't understand how you got that.
Let's see,\[\Large f(x)=5-4x\]\[\Large f(g(x))=5-4(2x+3)\]

Answer 23

Distributing the -4 gives us,\[\Large f(g(x))=5-8x-12\]

Answer 24

then u take the 5- 12?

Answer 25

@zepdrix

Answer 26

ya -8x-7