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Sonbull
2 months ago
15

Which of the following pairs of functions are inverses of each other?

Mathematics
2 answers:
PIT_PIT [12.4K]2 months ago
6 0

Answer:

D. The functions f(x)=8x³+6 and g(x)=³√(x-6)/8 are inverses of each other.

Explanation:

apex

babunello [11.8K]2 months ago
6 0

Answer:

The correct pair of inverse functions is:

Option: C

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Detailed explanation:

Two functions, f(x) and g(x), are inverses if:

f(g(x)) = g(f(x)) = x

which means the composition of the two functions results in the identity function regardless of the order.

A)

Given f(x)=\dfrac{x}{12}+15 and g(x)=12x-15, compute f(g(x)):

fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x

Thus, option A is incorrect.

B)

Given f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}, compute f(g(x)):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x

Thus, option B is incorrect.

D)

Given f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3, compute f(g(x)):

fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)

fog(x)=9+\sqrt[3]{9-x^3}\neq x

Thus, option D is incorrect.

C)

Given f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}, compute f(g(x)):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})

fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x

Similarly, compute g(f(x)):

gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x

Hence, option C is correct.

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Find three solutions for the linear equation 4x −3y = 1, and plot the solutions as points on a coordinate plane.
lawyer [12517]

Answer:

(1, 1), (2, 2.333) and (3, 3.666).

Step-by-step explanation:

To solve this equation, we can select various values for x and then compute the corresponding y values.

<pFor instance, when x = 1, we find:

4*1 - 3y = 1

3y = 3

y = 1

When x = 2, we discover:

4*2 - 3y = 1

3y = 7

y = 2.333

Then for x = 3, we have:

4*3 - 3y = 1

3y = 11

y = 3.666

Therefore, the coordinates we will plot are (1, 1), (2, 2.333), and (3, 3.666).

Refer to the attached image for the plot.

4 0
1 month ago
What is the solution to –4(8 – 3x) ≥ 6x – 8?
tester [12383]

Response:

x ≥ 4

Step-by-step breakdown:

Given

- 4(8 - 3x) ≥ 6x - 8 ← distribute the term in parentheses on the left side

- 32 + 12x ≥ 6x - 8 (subtract 6x from both sides)

- 32 + 6x ≥ - 8 (add 32 to both sides)

6x ≥ 24 (divide both sides by 6)

Thus, x ≥ 4

5 0
26 days ago
Read 2 more answers
A 2-column table with 10 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1,
PIT_PIT [12445]

Answer-  A,D,E

Step-by-step explanation:

A table featuring two columns with 5 rows. The first column, labeled x, contains the values: -2, 0, 2, 4. The second column, labeled y, includes the values: 6, 3.5, 1, -1.5.

Which equations correspond to the data shown in the table? Select all that apply.

y – 6 = -5/4(x + 2)

y – 2 = -5/4(x - 1)

y + 2 = -5/4(x - 6)

y – 1 = -5/4(x - 2)

y – 3.5 = -1.25x

This is just rewording the question

5 0
1 month ago
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Employee Number
Zina [12379]
The average years of employment is 14

with 73% having worked for at least 10 years.

To find the mean, add up the years of service and divide by the number of employees. The total years worked is 417, so the formula yields:

average years worked = 417/30 = 13.9, rounded to approximately 14 years.

To determine the percentage of employees with ten or more years, count those with 10 or more years and divide by the total employee count, converting the result into a percentage:

(10 years or over)/(total number) = 22/30 = 0.73 repeating, which approximates to 73%.

Using a spreadsheet tool can make this calculation simpler, as it can quickly compute the average and help tally how many employees have worked for 10 years or more.

3 0
13 days ago
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Ivan and Tanya share £150 in the ratio 4:1 how much more Ivan has then tanya
Zina [12379]

Hello!

--------------------------------------------------------

Solution:

The ratio is expressed as 4 to 1.

Add these parts together.

4 + 1 equals 5.

Now divide.

150 divided by 5 results in 30.

Next, multiply to find Ivan's share.

30 multiplied by 4 gives us 120.

30 multiplied by 1 equals 30 for Tanya.

Verify.

120 plus 30 totals 150.

Then subtract.

120 minus 30 equals 90.

--------------------------------------------------------

Answer:

Ivan possesses £90 more than Tanya!

--------------------------------------------------------

I hope this has been helpful! Best of luck!

3 0
1 month ago
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