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3 years ago

For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).

Mathematics

1 answer:

barxatty [35]3 years ago

7 0

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

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Can some please help with this? :)

den301095 [7]

Answer:

Step-by-step explanation:

The stuff that is yellow is the answer!

6 0

3 years ago

Domain and Range for the function f(x)=5IXI is

shutvik [7]

Answer:

The domain of the function f(x) is:

$\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

The range of the function f(x) is:

$\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}$

Step-by-step explanation:

Given the function

$f\left(x\right)=5\left|x\right|$

Determining the domain:

We know that the domain of the function is the set of input or arguments for which the function is real and defined.

In other words,

Domain refers to all the possible sets of input values on the x-axis.

It is clear that the function has undefined points nor domain constraints.

Thus, the domain of the function f(x) is:

$\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Determining the range:

We also know that range is the set of values of the dependent variable for which a function is defined.

In other words,

Range refers to all the possible sets of output values on the y-axis.

We know that the range of an Absolute function is of the form

$c|ax+b|+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k$

$k=0$

Thus, the range of the function f(x) is:

$\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}$

7 0

3 years ago

I will use fancy gold and red wrapping paper for two packages i have to wrap. I will use 1 2/4 yard of paper for one of the boxe

Allisa [31]

Well you need first 1 2/4 of a yard. Then you will need 5/6 of a yard. But first you need to put them together. So we need to find the common denominator. Six and four both share which multiple? Twelve. So let's rewrite that. You need 1 6/12 yards + 10/12 yards of wrapping paper. But before we do anything else we need to fix the mixed number. 1 6/12 isn't as easy to add ad 18/12 is. So 18/12 + 10/12 = 28/12
That can simplify as well. Now it's 14/6 which is equivalent to the fraction we had before. But it can also go down to 2 2/6. Now we can simplify it even further. By dividing it by two we can get 2 1/3. These are the measurements we need. So you would need how many thirds? Seven. (2 1/3 is seven thirds) This is your final answer.

You would need to have seven peices of wrapping paper cut to wrap both gift boxes.

6 0

3 years ago

Please help me! Please don't get it wrong ;-;

polet [3.4K]

Answer:

Its 40 degrees

Step-by-step explanation:

60+80=140

180-140=40 (a straight line is always 180 degrees)

Hope it helped

3 0

3 years ago

20 points if these are correct pls

kirza4 [7]

Step-by-step explanation:

14. 8

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16. 42

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20. 13

21. 18

5 0

3 years ago

Read 2 more answers