All categories

2 years ago

If f(x)=x-6 and g(x)=x^3, find G(f(x))

Mathematics

1 answer:

nika2105 [10]2 years ago

7 0

Answer:

$\boxed{\sf g(f(x)) = {x}^{4} - 6 {x}^{3}}$

Given:

$\sf f(x) =x - 6 \\ \sf g(x) = {x}^{3}$

To find:

$\sf g(f(x)) = f(x) \times g(x)$

Step-by-step explanation:

$\sf \implies g(f(x)) = f(x) \times g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (x - 6) \times ( {x}^{3} ) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ({x}^{3} \times x) - (6 \times {x}^{3}) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{4} - 6 {x}^{3}$

You might be interested in

Describe how (2 cubed) (2 superscript negative 4) can be simplified.

Varvara68 [4.7K]

<u>Given</u>:

The given expression is $(2^3)(2^{-4})$

We need to determine how the expression can be simplified.

<u>Simplifying the expression:</u>

Let us determine how the expression can be simplified.

The expression is given by

$(2^3)(2^{-4})$

Applying the exponent rule that $a^{b} \cdot a^{c}=a^{b+c}$ in the above expression, we get;

$2^{3} \cdot 2^{-4}=2^{3-4}$

Adding the exponents, we get;

$2^{3} \cdot 2^{-4}=2^{-1}$

Again, applying the exponent rule $a^{-1}=\frac{1}{a}$ , we get;

$2^{3} \cdot 2^{-4}=\frac{1}{2}$

Thus, the simplified expression is $\frac{1}{2}$

Hence, the expression is simplified by adding the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

Therefore, Option D is the correct answer.

8 0

2 years ago

Read 2 more answers

christy uses glass beads to make braclets and necklances it takes her 30 minutes to make a bracelet and 45 minites to make a nec

shtirl [24]

Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

<h3>How to determine how many bead of each type of bracelets and necklaces should Christy make to maximize his profit?</h3>

The given parameters can be represented in the following tabular form:

Bracelet (x) Necklace (y) Total

Labor (hour) 0.5 0.75 40

Profit 10 18

From the above table, we have the following:

Objective function:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

Because she wants to make at least 30 bracelets, we have:

x >= 30

So, we have:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

x >= 30

Express x >= 30 as equation

x = 30

Substitute x = 30 in 0.5x + 0.75y <= 40

0.5 * 30 + 0.75y <= 40

This gives

15 + 0.75y <= 40

Subtract 15 from both sides

0.75y <= 30

Divide by 0.75

y <= 40

Hence, Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

Read more about maximizing profits at:

brainly.com/question/13799721

#SPJ1

4 0

1 year ago

Please I need help step by step

zaharov [31]

To find the surface area, you need to do the following:
A side of the figure is a trapezoid, so you should do 13+5x7 (since there are 2 of the same sides there is no need to divide by two.) and it should equal 126. To find the area of the top of the figure, you need to do 5x2 which equals 10. The area of the bottom of the figure is 26 (13x2), then do 2x3x2 to get the sides on the left and right of the figure. After all of this, add them together. (126+10+26+12=174.)
The surface area should be 174mm.

6 0

2 years ago

The measure of the missing angle is ?

Cerrena [4.2K]

X = 97

Working on other question.

3 0

3 years ago

Which costs the most: 12 cat toys, 4 bags of cat food, or 3 litter boxes? Explain.

lukranit [14]

Answer:

3 litter boxes

Step-by-step explanation:

It depends what type it is

7 0

2 years ago