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2 years ago

Giving away brainly for help ASAP

Mathematics

1 answer:

Gelneren [198K]2 years ago

7 0

Answer:

$g(f(x))=25x^2-15x-7$

domain: (-∞,∞)

Step-by-step explanation:

g of f means plug the function f(x) in to x in the function g(x)

$g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7$

since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)

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<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%

Llana [10]

a) The given function is

$f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}$

The domain refers to all values of x for which the function is defined.

The function is defined for

$x^4+x^3-4x^2-4\ne0$

This implies that;

$x\ne -2.69,x\ne 1.83$

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

$x^4+x^3-4x^2-4=0$

This implies that;

$x= -2.69,x=1.83$

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

$\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

$\Rightarrow x^2-4=0$

$x^2=4$

$x=\pm \sqrt{4}$

$x=\pm2$

The roots are $x=-2,x=2$

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

$x=0$ into the function

$f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}$

$f(0)=\frac{-4}{-4}=1$

e) to find the horizontal asypmtote, we take limit to infinity

$lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

The horizontal asymtote is $y=0$

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0

3 years ago

What passes through (-2,5) and (3,9)

Harlamova29_29 [7]

Use maaaathhhhwwwaaayyy

It’s a lot better

3 0

3 years ago

Please help me if u give me an answer could u also give me an explanation on why that’s the answer.

Setler79 [48]

So it’s A

in all the other ones we can see that the angles in the same position as x and 75 are all equal

and because the question tells us that they are all structured the same with p and f being parallel we can assume x is equal to what’s congruent to it

there is a rule that states this

cap congruent angle postulate i believe

which states that if two parallel lines are cut by a transversal, then corresponding angles are congruent

7 0

3 years ago

Glenn needs 20 minutes to clean his room. If his little sister Veronika pulls things out while he is cleaning, it takes 60 minut

Bogdan [553]

Answer:

It takes 30 minutes

Step By Step:

The rate of Glenn in finishing a job would be equivalent to:

Rate (G) = 1

job / 20 minutes

While the rate of Veronika is:

Rate (V) = 1

job / x---> x is the unknown

Where 1 job for Glenn means completely cleaning his room while 1 job for Veronika means pulling out everything. Therefore the equation to use would be:

1 / 20 – 1 /

x = 1 / 60

The rate of

Veronika is subtracted from the rate of Glenn since Veronika is slowing Glenn

down. Solving for x:

Multiply both

sides by 60 x

(1 / 20 – 1 /

x = 1 / 60) * 60 x

3 x – 60 = x

2 x = 60

x = 30

Therefore it

takes 30 minutes for Veronika to pull everything out.

3 0

3 years ago

Simplify and expression for the perimeter of the the rectangle shown.

erma4kov [3.2K]

Answer:

Step-by-step explanation:

l = 8.6 x + 3

b = 5.2

perimeter =

6 0

2 years ago