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3 years ago

Which function is the inverse of f(x) =2x +3

Mathematics

2 answers:

frosja888 [35]3 years ago

5 0

Answer:

-1

f (x) = x/2 - 3/2

Step-by-step explanation:

I choose to address this question by actually finding the inverse of f(x) = 2x + 3.

1) replace f(x) with y: y = 2x + 3

2) interchange x and y: x = 2y + 3

3) solve this result for y: 2y = x - 3 , or y = (x - 3)/2. This is the same as the second answer choice. Label this result as

-1

f (x) = x/2 - 3/2

lesya692 [45]3 years ago

4 0

F(x)=
$f(x) = 2x + 3$
$let y = 2x + 3$
make y subject of the formula
$x = \frac{y - 3}{2}$
replace y with x above
$f ^{ - 1 } = \frac{x - 3}{2}$

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Maths!

Ber [7]

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

X $X-\bar X$ $(X-\bar X)^{2}$

5 5 - 8 = -3 9

8 8 - 8 = 0 0

10 10 - 8 = 2 4

9 9 - 8 = 1 1

6 6 - 8 = -2 4

Total 72 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{72}{9}$ = 8

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

X $X-\bar X$ $(X-\bar X)^{2}$

7 7 - 10 = -3 9

10 10 - 10 = 0 0

12 12 - 10 = 2 4

11 11 - 10 = 1 1

8 8 - 10 = -2 4

Total 90 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{90}{9}$ = 10

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the new standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.

4 0

4 years ago

In a circle with center C and radius 6, minor arc AB has a length of 4pi. What is the measure, in radians, of central angle ACB?

valina [46]

To solve this problem, we need to know that
arc length = r θ where θ is the central angle in radians.

We're given
r = 6 (units)
length of minor arc AB = 4pi
so we need to calculate the central angle, θ
Rearrange equation at the beginning,
θ = (arc length) / r = 4pi / 6 = 2pi /3

Answer: the central angle is 2pi/3 radians, or (2pi/3)*(180/pi) degrees = 120 degrees

8 0

3 years ago

Read 2 more answers

How many times larger is 8*10^6 than 2*10^2

bogdanovich [222]

The first step for solving this question is put both of your given expressions into one and then subtract them. This will look like the following:
8 × $10^{6}$ - 2 × 10²]
Now to make the calculation easier,, factor the expression.
(8 × $10^{4}$ - 2) × 10²
Evaluate the power inside the parenthesis.
(8 × 10000 - 2) × 10²
Evaluate the power outside the parenthesis.
(8 × 10000 - 2) × 100
Multiply the numbers inside the parenthesis.
(80000 - 2) × 100
Subtract the numbers in the parenthesis.
79998 × 100
Lastly,, multiply the numbers together to get your final answer.
7999800
This means that 8 × $10^{6}$ is 7999800 times larger than 2 × 10².
Let me know if you have any further questions.
:)

8 0

3 years ago

You have been advised to save 5% of your income for an emergency fund. How much would you have saved in one year, following the

Inessa [10]

You would save $2447.40 for the emergency fund

6 0

3 years ago

What is 6.9 divided by 58.65?

Alecsey [184]

Answer:

8.5

Step-by-step explanation: