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ELEN [110]
3 years ago
15

Please help me solve this...

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
7 0

Answer:

\displaystyle f(x)=\frac{5}{24}(x+2)^2(x-6)(x-2)

Step-by-step explanation:

The standard, factored polynomial function is given by:

f(x)=a(x-p)^n(x-q)^m...

Where <em>a</em> is the leading coefficient,

<em>p</em> and <em>q</em> are factors,

And <em>n </em>and <em>m</em> are the powers or multiplicity they are being raised to.

We know that our polynomial function is of degree 4.

We have a root of multiplicity of 2 at x=-2.

So, our factor is:

(x-(-2))=(x+2)\\

It is has a multiplicity of 2, it is squared. So:

(x+2)^2

We have another root with multiplicity of 1 at x=6.

So, our factor is:

(x-6)

And since it is to the first power, we can write it as is.

Finally, we have another root of multiplicity of 1 at x=2.

So, our factor is:

(x-2)

Therefore, our entire function is:

f(x)=a(x+2)^2(x-6)(x-2)

We still have to determine our leading coefficient, <em>a</em>.

We can use that y-intercept. The y-intercept is at (0, 10). So, when x=0, y=10. By substitution:

10=a(0+2)^2(0-6)(0-2)

Evaluate:

10=a(4)(-6)(-2)

Multiply:

10=48a

Therefore:

\displaystyle a=\frac{10}{48}=\frac{5}{24}

Therefore, our final function is:

\displaystyle f(x)=\frac{5}{24}(x+2)^2(x-6)(x-2)

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yulyashka [42]
I think it’s g^-1(x)= -2x+4

The “^” means exponent to -1 is the exponent of g

Hope I’m right !!
7 0
2 years ago
1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a
ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

1.

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

2.

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

3.

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

4.

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

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3 years ago
Bella’s shoe is more or less than one yard?
Luba_88 [7]
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Therefore, Bella's shoe is less than one yard.

Hope this helps! :)
3 0
3 years ago
If a student was randomly guessing while completing a 20 question multiple choice exam, what is the probability they would score
mario62 [17]

Answer:

you want 4 correct and 16 incorrect

there are 20 questions

each question has four answers, so

P(right answer) = 1/4

P(wrong answer) = 3/4

----

Since you want 4 correct of 20 we have a combination of 20C4

This is a binomial problem where p = 1/4, q = 3/4 and we get

(20 "choose" 4)*(probability correct)^(number correct)*(probability incorrect)^(number incorrect)

putting numbers in we get

(20c4)*(1/4)^4*(3/4)^16

This gives us

~ .189685

Step-by-step explanation:

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Debora [2.8K]

Answer:

Step-by-step explanation:

stop cheating lololololol

3 0
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