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Verizon [17]
2 years ago
15

What are the correct answers and why? Simple and concise explanation please!!!

Mathematics
2 answers:
dezoksy [38]2 years ago
6 0

Answer:

\large\boxed{-\bigg[(x-3)^2+2x\bigg]+1}\\\\\boxed{-x^2+4x-8}

Step-by-step explanation:

(g\ \circ\ f)(x)=g\bigg(f(x)\bigg)

f(x)=(x-3)^2+2x\\\\g(x)=-x+1\\\\g\ \circ\ f\to\text{put f(x) instead of x in the function g(x)}:\\\\(g\ \circ\ f)(x)=-\bigg[\underbrace{(x-3)^2+2x}_{x}\bigg]+1

-----------------------------------------

-\bigg[(x-3)^2+2x\bigg]+1=-(x-3)^2-2x+1\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=-(x^2-(2)(x)(3)+3^2)-2x+1=-(x^2-6x+9)-2x+1\\\\=-x^2-(-6x)-9-2x+1=-x^2+6x-9-2x+1\\\\\text{combine like terms}\\\\=-x^2+(6x-2x)+(-9+1)=-x^2+4x-8

-----------------------------------

-x^2+4x-8=-x^2+4x-2^2+2^2-8=-(x^2-4x+2^2)+4-8\\\\=-(\underbrace{x^2-(2)(x)(2)+2^2}_{(a-b)^2=a^2-2ab+b^2})-4=-(x-2)^2-4=-(x+1-3)^2-4

In\ (-x+1-3)^2+2x,\ x^2\ will\ be\ positive.\\In\ (-x+1-3)^2+2(-x+1),\ x^2\ will\ be\ positive.

Gre4nikov [31]2 years ago
4 0

Answer:

1st 4th

Step-by-step explanation:

Remark

g ° f has the meaning of

"look at g(x) where ever there is an x in g(x) put all of f(x) where that x is."

g(f(x)) = - f(x) + 1

Choice One

g(f(x)) = - [(x - 3)^2 + 2x] + 1 which is exactly what g(f(x)) comes down to.

Choice 4

g(f(x)) = - [(x - 3)^2 + 2x] + 1

g(f(x)) = - [x^2 - 6x + 9] + 1

g(f(x)) = - x^2 + 6x - 9 + 1

g(f(x)) = - x^2 + 6x - 8

The others.

Some of them are

f(g(x))

Number 2 is half that way.

f(g(x)) = (g(x) - 3)^2 + 2(g(x)) is what it should be if f(g(x)) was what you were asked for the 2x has no substitution made. In any event, choice 2 is incorrect.

I'm not sure how three was obtained. It is not correct if one and four are.

Same comment applies to five. I'm not sure how it was obtained.

Number six is f(g(x)) You have it backwards.

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For all values of x
Yuliya22 [10]

Answer:

A.) gf(x) = 3x^2 + 12x + 9

B.) g'(x) = 2

Step-by-step explanation:

A.) The two given functions are:

f(x) = (x + 2)^2 and g(x) = 3(x - 1)

Open the bracket of the two functions

f(x) = (x + 2)^2

f(x) = x^2 + 2x + 2x + 4

f(x) = x^2 + 4x + 4

and

g(x) = 3(x - 1)

g(x) = 3x - 3

To find gf(x), substitute f(x) for x in g(x)

gf(x) = 3( x^2 + 4x + 4 ) - 3

gf(x) = 3x^2 + 12x + 12 - 3

gf(x) = 3x^2 + 12x + 9

Where

a = 3, b = 12, c = 9

B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)

To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

Y = 3x + 3

X = 3y + 3

Make y the subject of formula

3y = x - 3

Y = x/3 - 3/3

Y = x/3 - 1

Therefore, g'(x) = x/3 - 1

For g'(12), substitute 12 for x in g' (x)

g'(x) = 12/4 - 1

g'(x) = 3 - 1

g'(x) = 2.

5 0
2 years ago
What is h=3.6 what h
emmainna [20.7K]

Answer:

3.6 since h = 3.6

Step-by-step explanation:

5 0
3 years ago
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I need help bad I will mark you as king or what every pkz get it right I can’t get it right plz help
Ostrovityanka [42]

Answer:

d=6c it looks like. good luck

4 0
2 years ago
Need help asap!! Thank u
fiasKO [112]

Step-by-step explanation:

There is 10 questions which in this case are the trials.

We know we can either get a question right or wrong so the two outcomes are right or wrong.

The probability that a student choose the right outcome is 1/4. since there is one right answer out of 4 chocies.choices.

Yes, the trials likelihood outcome of each outcome is the same. so it's independent

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2 years ago
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Answer:29503.49

Step-by-step explanation:

7 0
2 years ago
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