Write the equation for a line that is perpendicular to the line y = −2?

Consider the function f(x) = 8x^3 +1. If f(g(x)) = x and g(f(x)) = x , find g(x) ?

Elena L [17]

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

And

$f( \: g(x) \: ) = x$ _________________________________

So :

$g(x) = {f}^{ - 1}(x)$

And

$f(x) = {g}^{ - 1}(x)$

_________________________________

So to find g(x) , we must find the inverse of f(x) .

Let's do it .....

$f(x) = 8 {x}^{3} + 1$

$y = 8 {x}^{3} + 1$

Subtract the sides of the equation minus 1

$y - 1 = 8 {x}^{3}$

Divided the sides of the equation by 8

$\frac{y - 1}{8} = {x}^{3} \\$

From the sides of the equation, we take the radical with interval 3

$\sqrt[3]{ \frac{y - 1}{8} } = x \\$

$\sqrt[3]{ \frac{1}{8}(y - 1) } = x \\$

$\frac{1}{2} \sqrt[3]{y - 1} = x \\$

$\frac{ \sqrt[3]{y - 1} }{2} = x \\$

So ;

${f}^{ - 1}(x) = \frac{ \sqrt[3]{x - 1} }{2} \\$

Now we find g(x) which is :

$g(x) = \frac{ \sqrt[3]{x - 1} }{2} \\$

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

7 0

3 years ago

What is the probability of spinning an A? B B A B C A [?]% C

siniylev [52]

Answer:

25%

Step-by-step explanation:

when we count, we know that there are 8 possible outcomes as to where the spinner will land.

{the following will be assuming each section has an equal chance of being landed on; that the spinner is not weighted}

We know that two of these 8 possibilities are "A"

This means that A has a 2/8 chance of being landed on

we can simplify 2/8 to 1/4; because they are equivalent ratios/fractions

to calculate percentage, we can follow through with our equation of 1/4

[divide 1 by 4]

1 / 4 = 0.25

We multiply this number by 100 to find percentage,

0.25 × 100 = 25

meaning that A has a 25% chance of being spun

hope this helps!! have a lovely day :)

8 0

2 years ago

Read 2 more answers

Round number to the nearest hundreds 748

Triss [41]

700 because 48 is under 50 which makes it have to round down to the nearest hundred

6 0

4 years ago

Symbolism uses a concrete image to convey something that is what? Choices are: 1. lost. 2. intangible. 3. tangible. 4. uncertain

Shalnov [3]

I believe the correct answer from the choices listed above is option 2. Symbolism uses a concrete image to convey something that is intangible. It is an object representing another to give it an entirely different meaning that is much deeper and more significant.

8 0

3 years ago

Read 2 more answers

I need to understand this kindly help.....

AveGali [126]

Answer:

Section a)

Solution;

A correlation coefficient of 0.4 implies a relatively weak positive association between two sets of data. There is a notable small increment in one data set as the other increases.

Section b)

Solution;

A correlation coefficient of -0.96 implies a strong negative association between two sets of data. An increase in the values of one data set amounts to a decrease in the values of the other data set by approximately the same magnitude.

Section c)

Solution;

A correlation coefficient of -0.02 implies a weak negative association between two sets of data. An increase in the values of one data set amounts to a negligible decrease in the values of the other data set.

Section d)

Solution;

A correlation coefficient of 1.0 implies a perfect positive association between two sets of data. An increase in the values of one data set amounts to an increase in the values of the other data set by exactly the same magnitude. A scatter plot would reveal that the line y =x fits the data well.

Section e)

Solution;

A correlation coefficient of 0.86 implies a strong positive association between two sets of data. An increase in the values of one data set amounts to an increase in the values of the other data set by approximately the same magnitude.

Step-by-step explanation:

Correlation coefficient measures the degree of association between two variables or data sets. Correlation coefficients can be positive or negative and may imply weak or strong association between two data sets.

A correlation coefficient of less than 5 is implies a weak association while a value greater than or equal to 5 implies a strong association. Finally, a correlation of 1.0 implies perfect association.

7 0

3 years ago