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2 years ago

If f(x) = one/nine x -2, what is f^-1(x)

Mathematics

1 answer:

astraxan [27]2 years ago

6 0

Answer:

$f^{-1} (x)=9x+18$

Step-by-step explanation:

Assuming $f(x)=\frac{1}{9} x-2$

What we have to do is replace f(x) with y, swap the locations of x and y, and then solve for y.

$y= \frac{1}{9} x-2\\\\x=\frac{1}{9}y-2\\ \\x+2=\frac{1}{9}y\\\\y=9x+18\\\\f^{-1} (x)=9x+18$

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Select the correct answer.

Radda [10]

Answer:

$(-1\frac{1}{3}, 4\frac{3}{5})$

Step-by-step explanation:

To find the exact solution, find the equation for each line. And solve for x and y.

To do this, represent each equation in the slope-intercept form, y = mx + b. Where m is the slope, and b is the y-intercept.

✍️Equation 1 for the line that slopes upwards from left to your right:

Slope = $m = \frac{rise}{run} = \frac{2}{1} = 2$

b = the point at which the y-axis is intercepted by the line = 7

Substitute m = 2 and b = 7 in y = mx + b

Equation 1 would be:

✔️y = 2x + 7

✍️Equation 2 for the line that slopes downwards from left to your right:

Slope = $m = \frac{rise}{run} = -\frac{3}{1} = -3$

b = the point at which the y-axis is intercepted by the line = 1

Substitute m = -3 and b = 1 in y = mx + b

✔️Equation 2 would be:

y = -3x + 1

✍️Solve for x and y:

✔️To solve for x, substitute y = -3x + 1 in equation 1.

y = 2x + 7

-3x + 1 = 2x + 7

Collect like terms

-3x - 2x = 7 - 1

-5x = 6

Divide both sides by -5

$x = \frac{6}{-5} = -1\frac{1}{5}$

✔️To solve for y, substitute x = -1⅕ in equation 2.

y = -3x + 1

$y = -3\frac{-6}{5} + 1$

$y = \frac{18}{5} + 1$

$y = \frac{18 + 5}{5}$

$y = \frac{23}{5}$

$y = 4\frac{3}{5}$

✅The exact solution would be: $(-1\frac{1}{3}, 4\frac{3}{5})$

3 0

2 years ago

I got the first two can you help me with the last one PLZ

Nat2105 [25]

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

$a_1 =6\\a_2 = 18\\a_3 = 54$

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

$r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3$

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

$a_n = a_{n-1} * r$

In case of given sequence,

$a_n = a_{n-1} * 3$

So to find the 5th term

$a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486$

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

$a_n = a_1 * r^{n-1}$

Putting the values of a_1 and r

$a_n = 6 * (3)^{n-1}$

Hence,

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

#LearnwithBrainly

4 0

3 years ago

Mercury has a density of 13.6 g/mL. A sample of mercury weighs 2.25 kg. What volume does it occupy

laila [671]

Answer:

165 mL

Step-by-step explanation:

Density is mass divided by volume:

D = M / V

Solving for volume:

V = M / D

The density is given in g/mL. So first let's convert the mass from kg to g:

2.25 kg × (1000 g / kg) = 2250 g

Plugging in values:

V = (2250 g) / (13.6 g/mL)

V = 165.4 mL

Rounded to 3 significant figures, the volume is 165 mL.

8 0

3 years ago

My math problem dealing with fractions ask What is 1/8 of 9?

Norma-Jean [14]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Skylar plans to use $3400 to open a savings account with an annual interest rate of 1.15%. How much more interest will he earn o

Tanzania [10]

Answer:

$ 2.5

Step-by-step explanation:

Given that

Total Amount to be invested = P = $3400

Total Time of investment = t = 13 years

Rate of interest = r = 1.15 %

Lets calculate Simple interest first

As we know formula for simple interest is

$A = P (1 +r)^{t}$

Substituting the values

$A = 3400(1+ \frac{1.15}{100} )^{13}$

A = $ 3944.9

Lets now calculate the compound interest

As we know formula for simple interest is

$A = P (1 + \frac{r}{n})^{nt}$

As compound interest applies every 3 months so n =3

So,

$A = 3400 (1 + \frac{1.15}{100*4} )^{13*4}$

A = $ 3947.4

Now Lets calculate how much more he will earn using compound interest.

It can be found by taking difference of compound interest and simple interest

Amount = 3947.4 - 3944.9 = $ 2.5

So Skyler must have earned 2.5 dollar more using the compound interest.

8 0

2 years ago