anonymous
  • anonymous
Use the functions f(x) = 5x − 12 and g(x) = 11x + 2 to complete the function operations listed below. Part A: Find (f + g)(x). Show your work. (3 points) Part B: Find (f ⋅ g)(x). Show your work. (3 points) Part C: Find f[g(x)]. Show your work. (4 points)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@Keigh2015
anonymous
  • anonymous
@phi
anonymous
  • anonymous
Hey

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Keigh2015
  • Keigh2015
do you have an idea for it yet?
phi
  • phi
(f + g)(x) that is short of adding f(x) + g(x)
anonymous
  • anonymous
so add 5x − 12 And 11x + 2
phi
  • phi
and f(x)+g(x) is short for: write down the "formula" for f(x) and add it to the "formula" for g(x) yes
Keigh2015
  • Keigh2015
yes i believe
phi
  • phi
B is the same idea except you multiply (use FOIL to multiply it out)
anonymous
  • anonymous
let me add the first one real quick hold on
phi
  • phi
can you do parts A and B?
anonymous
  • anonymous
16x−10
phi
  • phi
yes
anonymous
  • anonymous
Yea i think so, ill try could you check my work?
phi
  • phi
for part C f[g(x)] means "in the formula for f(x), replace "x" with g(x)"
anonymous
  • anonymous
for part B i got 55x2−122x−24 i think thats wrong
phi
  • phi
too bad, I got the same thing.
anonymous
  • anonymous
is it?
phi
  • phi
yes, you did it correctlly
anonymous
  • anonymous
ill just put that as the answer, because i honestly have to clue.
anonymous
  • anonymous
ooh yay okay
phi
  • phi
you can check that it is correct. pick a number for x, such as 1 then f(x) = 5x − 12 at x=1 is 5-12= -7 and g(x) = 11x + 2 at x=2 is 11+2 = 13 and -7*13= -91 now use your formula 55x^2−122x−24 at x=1... you get 55 -122 -24 = -91 same number. that does not prove it, but if you did that for a few values, and it always works, it probably is correct.
anonymous
  • anonymous
for part c, questions like that confuse me cause i never learned the foil method.
anonymous
  • anonymous
@phi
anonymous
  • anonymous
@Keigh2015
Keigh2015
  • Keigh2015
that one confuses me too
anonymous
  • anonymous
@mathstudent55
phi
  • phi
but if you FOIL it: ( 5x − 12) (11x+2) F first: 5x*11x = 55x^2 O outer: 5x*2 = 10x I inner: -12*11x = -132x L last: -12*2 = -24 combine the two middle terms 10x-132x = -122 x and the answer is 55x^2 -122x -24
anonymous
  • anonymous
@mathstudent55 i need help with part c
phi
  • phi
part C f[g(x)] first write down f(x)
anonymous
  • anonymous
5x − 12
phi
  • phi
like this f(x)=5x − 12 we want f[g(x)] that means erase the x and replace it with g(x) erase and replace: f( g(x) ) = 5g(x) -12
phi
  • phi
then replace g(x) with g(x)'s formula (11x + 2) be sure to use the parens
phi
  • phi
can you replace g(x) in 5g(x) -12 with (11x+2)
anonymous
  • anonymous
f( 11x + 2) = 5(11x + 2) -12
anonymous
  • anonymous
@phi
phi
  • phi
yes, but we usually leave the left side in "short form" f(g(x)) and only expand the right side but yes that looks good. you can distribute the 5 (multiply 5 times each thing inside the parens) and simplify the right side a little.
anonymous
  • anonymous
x=1\11 ? @phi
phi
  • phi
the right side is 5(11x + 2) -12 do 5 * 11x + 5*2 to distribute the 5 55x + 10 -12 now simplify 10-12
anonymous
  • anonymous
-2?
phi
  • phi
yes. so part C is f[g(x)]= 55x-2
anonymous
  • anonymous
Yay thankyou @phi

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