anonymous
  • anonymous
Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (f o g)(-5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jim_thompson5910
  • jim_thompson5910
(f o g)(-5) is the same as f(g(-5)) the first task is to find g(-5). Do you know how to do this?
anonymous
  • anonymous
A. -53 C.23 D.3
anonymous
  • anonymous
No i have no clue

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anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
Could you help @jim_thompson5910
anonymous
  • anonymous
@SolomonZelman
jim_thompson5910
  • jim_thompson5910
g(x) = -4x + 3 g(-5) = -4(-5) + 3 ... replace every x with -5 g(-5) = ??
misssunshinexxoxo
  • misssunshinexxoxo
On OS we help people learn; Jim is trying to make sure you are understanding this
anonymous
  • anonymous
Oh i know and i defiantly want the help
UsukiDoll
  • UsukiDoll
(f o g)(-5) well first let's do (f o g ) which means that the g(x) equation is placed inside the f(x) equation
anonymous
  • anonymous
20+3
UsukiDoll
  • UsukiDoll
whoa... let's do this step by step
anonymous
  • anonymous
Oh sorry i was replying to what @jim_thompson5910 started
jim_thompson5910
  • jim_thompson5910
so you should find that g(-5) = 23 agreed?
anonymous
  • anonymous
correct
jim_thompson5910
  • jim_thompson5910
f(g(-5)) becomes f(23) after you replace g(-5) with 23
jim_thompson5910
  • jim_thompson5910
now follow the same basic steps to calculate f(23)
UsukiDoll
  • UsukiDoll
ok it's ok didn't see that :) anyway given the functions f(x) = -2x-7 and g(x) = -4x+3 we need to place g(x) =-4x+3 into the f(x) so for every x in f(x) the g(x) takes it's place
UsukiDoll
  • UsukiDoll
so the end result should be -2(insert g(x) function here)-7
UsukiDoll
  • UsukiDoll
then combine like terms and evaluate when x = -5
anonymous
  • anonymous
im lost
anonymous
  • anonymous
Is the answer 23?
jim_thompson5910
  • jim_thompson5910
no
UsukiDoll
  • UsukiDoll
I agree with jim there's more to be done...
anonymous
  • anonymous
ok im ready to learn the rest
UsukiDoll
  • UsukiDoll
k.. so did you already place your g(x) into your entire f(x) function?
anonymous
  • anonymous
No i got lost after we got f(23)
jim_thompson5910
  • jim_thompson5910
To calculate f(23), replace every x in f(x) with 23 f(x) = -2x - 7 f(23) = -2*23 - 7 f(23) = ??
UsukiDoll
  • UsukiDoll
that means x = 23 evaluate the f(x) function
jim_thompson5910
  • jim_thompson5910
it's just like the g(x) one
anonymous
  • anonymous
-46
anonymous
  • anonymous
f(23)=-46-7
jim_thompson5910
  • jim_thompson5910
keep going
UsukiDoll
  • UsukiDoll
almost there
anonymous
  • anonymous
46-7=39
UsukiDoll
  • UsukiDoll
we have two negative numbers so the negative numbers are supposed to increase, not decrease
anonymous
  • anonymous
opps wrong
anonymous
  • anonymous
-53
UsukiDoll
  • UsukiDoll
yes!
jim_thompson5910
  • jim_thompson5910
good
UsukiDoll
  • UsukiDoll
do you want to see another method of solving this equation as a reference?
anonymous
  • anonymous
yay we did it
anonymous
  • anonymous
yes that would be great
UsukiDoll
  • UsukiDoll
ok so here's how I would tackle this problem (f o g ) (-5) first I will tackle f o g portion and then evaluate when x = -5 so f o g means that we place our g(x) function inside all x's of the f(x) function f(x) = -2x-7 and g(x) = -4x+3 f o g -2(-4x+3)-7 distribute the -2 8x-6-7 8x-13 so our f o g = 8x-13 now evaluating when x = -5 f o g (-5) = 8(-5)-13 = -40-13 = -53
anonymous
  • anonymous
Can you guys help me solve another @UsukiDoll @jim_thompson5910
UsukiDoll
  • UsukiDoll
sure
anonymous
  • anonymous
Let f(x) = x + 2 and g(x) = x2 Find ( g o f)(-5)
UsukiDoll
  • UsukiDoll
\[\large f(x) = x+2, g(x) = x^2 \]
UsukiDoll
  • UsukiDoll
this is similar to the previous problem. while our x still remains the same g o f means that we place our entire f(x) function inside the x's of the g(x) function so g o f = (insert f(x) here)^2
anonymous
  • anonymous
so is x -2?
UsukiDoll
  • UsukiDoll
our f(x) = x+2 and we need place it inside g(x). Since g(x) =x^2 g o f = (f(x) function)^2
anonymous
  • anonymous
so X^2+X+2?
UsukiDoll
  • UsukiDoll
\[g o f =(x+2)^2 \] that second power means write (x+2) two times after that, we need to use FOIL to expand
anonymous
  • anonymous
your gonna have to hold my hand on this one cuz im totally lost lol im sorry
UsukiDoll
  • UsukiDoll
alirght.. so we write (x+2) two times (x+2)^2 means (x+2)(x+2) now using FOIL (x)(x)+2(x)+2(x)+(2)(2) so what's 2 x 2 2x + 2x and x times x I guess that's the closest way of notating multiplication
anonymous
  • anonymous
Ok so where do we go from this?
UsukiDoll
  • UsukiDoll
first tell me what 2 x 2 is then tell me what 2x+2x is .. I will factor out the x to make it easier x(2+2)
anonymous
  • anonymous
2x2=4
anonymous
  • anonymous
2x+2x=4X
UsukiDoll
  • UsukiDoll
mhm last one what is (x)(x) . I'll make this easier by rewriting it and using the addition exponential rule, \[\large (x)(x) \rightarrow x^1x^1 \rightarrow x^{1+1}\] so you just have to solve for the exponent part. what is 1+ 1
anonymous
  • anonymous
2
anonymous
  • anonymous
\[x ^{2}\]
UsukiDoll
  • UsukiDoll
yes so now we have \[g o f =x^2+4x+4 \]
UsukiDoll
  • UsukiDoll
so now we evaluate this when x = -5. so replace all x's with -5
anonymous
  • anonymous
25-20+4=9
UsukiDoll
  • UsukiDoll
\[g o f (-5) =(-5)^2+4(-5)+4\] \[g o f (-5) =25-20+4 \rightarrow 5+4 = 9 \] correct
anonymous
  • anonymous
Thank you very much

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