MATHEMATICS COLLEGE

F(x)=2

x

2

−

5

x

−

8

2x

2

−5x−8

g

(

x

)

=

g(x)=

−

5

x

+

4

−5x+4

Find:

(

g

∘

f

)

(

x

)

Find: (g∘f)(x)

Answers

Answer 1

Answer:

Answer:

$(g\ o\ f)(x) = -10x^2 + 25x + 44$

Step-by-step explanation:

Given

$f(x) = 2x^2 - 5x - 8$

$g(x) = -5x+4$

Required

$Find:\ (g\ o\ f)(x)$

In functions;

$(g\ o\ f)(x) = g(f(x))$

Substitute $f(x) = 2x^2 - 5x - 8$ in $(g\ o\ f)(x) = g(f(x))$

$(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))$

Solving for $g(f(2x^2 - 5x - 8))$

If $g(x) = -5x+4$

then

$g(f(2x^2 - 5x - 8)) = -5(2x^2 - 5x - 8) + 4$

Open Bracket

$g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 40 + 4$

$g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 44$

Recall that:

$(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))$

This implies that

$(g\ o\ f)(x) = -10x^2 + 25x + 44$

Related Questions

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Of the 35 jewelers in her town, Naomi polled the 5 biggest to learn about the latest jewelry trends. Her sample is . The sample is of the jewelers in Naomi’s town.
Which pair of variables would most likely have a negative correlation?A. the time spent driving in a car and the number of miles drivenB. the height of a dog in inches and the number of ounces of food the dog eats per dayC. the number of sit-ups completed and the number of calories burned during a workoutD. the time spent reading a book and the number of pages remaining to be read in the book

-3=?-11 Find the missing value.

Answers

Answer:

?=8

Step-by-step explanation:

I substituted the ? for x

-3=x-11

first we want to isolate the x to do that, you have to find a way to move -11 to the other side. Well, x+0=x right? So all we have to do is find a way to go from -11 to 0! In this case you add 11 to both sides. This is very important so don't forget.

-3=x-11

+11 +11

-3+11=8

x=8

If you check your work, this should also go back in perfectly.

-3=8-11

-3=-11+8

I hope this helps!

Have a good day!

A square has sides of 16 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x. V(x)=

Answers

A distance of (x+1) is cut in from both sides, so the base dimensions are

... 16 -2(x+1) = 14-2x

The depth of the fold is (x+1), so that is the depth of the box.

The volume is ...

... V(x) = (x+1)(14 -2x)²

Suppose you wanted to estimate the difference between two population means correct to within 4.8 at the 92% confidence level. If prior information suggests that both population variances are approximately equal to 12 and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?Critical Value: 1.75
The sample sizes should be: n1=___n2=_____?

Answers

Answer: $n_1=n_2=4$

Step-by-step explanation:

Given : Margin of error : E= 4.8

Confidence level : 92%

Significance level : $1-0.92=0.08$

$\sigma_1^2=\sigma_1^2\approx12$

Two-tailed critical value :-

$z_(\alpha/2)=z_(0.08/2)=z_(0.04)=1.75$

If we want to select independent random samples of equal size from the populations,

Formula for the sample size :

$n_1=n_2=((z_(\alpha/2))/(E))^2(\sigma_1^2+\sigma_2^2)$

Then buy using given values , we have

$n_1=n_2=((1.75)/(4.8))^2(12+12)$

Simplify ,

$n_1=n_2=((1.75)/(4.8))^2(12+12)=3.190\approx4$ [Round to the next integer.]

Hence, the The sample sizes should be: $n_1=n_2=4$

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?8 оооо
4

Answers

Answer:

x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)

thus :

Step-by-step explanation:

Solve for x over the real numbers:

x^2 - 8 x - 4 = 0

Hint: | Solve the quadratic equation by completing the square.

Add 4 to both sides:

x^2 - 8 x = 4

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 16 to both sides:

x^2 - 8 x + 16 = 20

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 4)^2 = 20

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 4 = 2 sqrt(5) or x - 4 = -2 sqrt(5)

Hint: | Look at the first equation: Solve for x.

Add 4 to both sides:

x = 4 + 2 sqrt(5) or x - 4 = -2 sqrt(5)

Hint: | Look at the second equation: Solve for x.

Add 4 to both sides:

Answer: x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)

Answer:

-8 or option A

Step-by-step explanation:

2023

Brand X batteries have a mean life span of 102 hours, with a standard deviation of 6.8 hours. Brand Y batteries have a mean life span of 100 hours, with a standard deviation of 1.4 hours. Complete each of the sentences.

Answers

Answer:

Step-by-step explanation:

Hello!

X₁: Life span of a battery of Brand X

X₁~N(μ₁;σ₁²)

μ₁= 102hours

σ₁= 6.8hours

X₂: Life span of a battery of Brand Y

X₂~N(μ₂;σ²)

μ₂= 100hours

σ₂= 1.4hours

To complete the first two sentences, you have to use the empirical rule:

μ±δ= 68% of the distribution

μ±2δ= 95% of the distribution

μ±3δ= 99% of the distribution

1. About 68% of brand x’s batteries have a lifespan between 95.2 and 108.8 hours.

μ₁±σ₁= 102 ± 6.8= 95.2; 108.8

2. About 68% of brand y’s batteries have a lifespan between 98.6 and 101.4 hours.

μ₂±σ₂= 100 ± 1.4= 98.6; 101.4

3. The life span of brand Y ’s battery is more likely to be consistently close to the mean.

The standard deviations show you the dispersion of the distribution. A low standard deviation indicates that the values are close to the mean. A high standard deviation indicates that the values are further away the values are from the mean.

The standard deviation for the X batteries is σ₁= 6.8hours and the Y batteries are σ₂= 1.4hours since the standard deviation for the Y batteries is less than the standard deviation for the X batteries, you'd expect that the life span of the Y batteries will be closer to the mean than the life span of the X batteries.

I hope it helps!

Consider the series 4+8+16+32+...
What is the common ratio?