anonymous
  • anonymous
f(x)= 2x+3 g(x) = 5 - 4x x=4 Solve for f(g(x)) and g(f(x))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
\[\Large f(x)=2x+3 \qquad \qquad g(x)= 5-4x\qquad\qquad x=4\] Hmm I'm trying to figure out why they included x=4. They probably meant that they want us to solve for, \(\large f(g(4)) \qquad\text{and}\qquad g(f(4))\)
zepdrix
  • zepdrix
\[\Large f(\color{royalblue}{x})=2\color{royalblue}{x}+3\]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,\[\Large f(\color{royalblue}{g(x)})=2\color{royalblue}{(5-4x)}+3\]
zepdrix
  • zepdrix
If we wanted to evaluate this at x=4, we have,\[\Large f(\color{royalblue}{g(4)})=2\color{royalblue}{(5-4\cdot4)}+3\]

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zepdrix
  • zepdrix
What do you think Crys? :x too confusing?
anonymous
  • anonymous
No I get the concept! :)
anonymous
  • anonymous
Will the answer be 11? @zepdrix
zepdrix
  • zepdrix
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
anonymous
  • anonymous
yea i used calculator
zepdrix
  • zepdrix
\[\Large \color{royalblue}{g(4)=5-4\cdot4=-11}\]\[\Large \color{royalblue}{g(4)=-11}\] We want to plug this value in for f(x).
zepdrix
  • zepdrix
\[\Large f(\color{royalblue}{g(4)}) \qquad=\qquad f(\color{royalblue}{-11})\]
zepdrix
  • zepdrix
\[\Large f(-11)=2(-11)+3\]
anonymous
  • anonymous
Ok I see how I get -19 now!
zepdrix
  • zepdrix
Function notation so confusing! :) Takes a little getting used to. Try to find your g(f(4)) also
anonymous
  • anonymous
I just did pemdas
anonymous
  • anonymous
Ok Ill let u know what I get
anonymous
  • anonymous
So will it start out with 5-4x(2x+3)
zepdrix
  • zepdrix
5-4(2x+3) careful, i see an extra x in there! :O we `replace` the x with that big mess of parentheses.
anonymous
  • anonymous
how is that?
anonymous
  • anonymous
ohhhh i seee lol
anonymous
  • anonymous
distrubuted and got 10x +15 -8x-12
anonymous
  • anonymous
do i sub the 4 now?
zepdrix
  • zepdrix
oh sorry i disappeared there +_+ Hmmm i don't understand how you got that. Let's see,\[\Large f(x)=5-4x\]\[\Large f(g(x))=5-4(2x+3)\]
zepdrix
  • zepdrix
Distributing the -4 gives us,\[\Large f(g(x))=5-8x-12\]
anonymous
  • anonymous
then u take the 5- 12?
anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
ya -8x-7

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