All categories

3 years ago

Determine the inverse of the function. (show work please)

Mathematics

1 answer:

uysha [10]3 years ago

5 0

Answer:

This is easy -- it's just a list of steps. At this level, the problems are pretty simple.

Let's just do one, then I'll write out the list of steps for you.

Find the inverse of f( x ) = -( 1 / 3 )x + 1

STEP 1: Stick a "y" in for the "f(x)" guy:

y = -( 1 / 3 )x + 1

STEP 2: Switch the x and y

( because every (x, y) has a (y, x) partner! ):

x = -( 1 / 3 )y + 1

STEP 3: Solve for y:

x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3

STEP 4: Stick in the inverse notation, f^( -1 )( x )

f^( -1 )( x ) = -3x + 3

Step-by-step explanation:

You might be interested in

17 13/18 divided by 2 7/9

erik [133]

let's firstly convert the mixed fractions to improper fractions and then divide.

$\bf \stackrel{mixed}{17\frac{13}{18}}\implies \cfrac{17\cdot 18 +13}{18}\implies \stackrel{improper}{\cfrac{319}{18}}~\hfill \stackrel{mixed}{2\frac{7}{9}}\implies \cfrac{2\cdot 9+7}{9}\implies \stackrel{improper}{\cfrac{25}{9}} \\\\[-0.35em] ~\dotfill$

$\bf \cfrac{319}{18}\div \cfrac{25}{9}\implies \cfrac{319}{\underset{2}{~~\begin{matrix} 18 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{1}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{25}\implies \cfrac{319}{50}\implies 6\frac{19}{50}$

7 0

3 years ago

the directions are : find the constant of proportionality for the graph and write in the form y = kx.n

Lelechka [254]

here is the answer (A) y=1/5 x

5 0

3 years ago

Robert accepted a new job at a company with a contract guaranteeing annual raises. Let S represent Robert's salary after working

vesna_86 [32]

Answer:

74,000

Step-by-step explanation:

In the year where he got 104,000 the year before he got 6,000 less. The year before 98,000 he got 12,000 less which means that now it would just be 86,000-12,000=74,000

I think this is right but you can double check on a calculator

Hope this helped!

6 0

2 years ago

You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery

riadik2000 [5.3K]

Answer:

Loss of $1.20

Step-by-step explanation:

The possible outcomes for this lottery and their probabilities are:

- a 1 in 100 chance of winning $450

- a 2 in 100 chance of winning $120

- a 4 in 100 chance of winning $30

- a 93 in 100 chance of losing $10

Therefore, the expected value of this lottery when buying one ticket is:

$E(X) = \frac{1}{100}*\$450+ \frac{2}{100}*\$120+ \frac{4}{100}*\$30-\frac{93}{100}*\$10 \\E(X) = -\$1.2$

Therefore, you are expected to lose $1.2 per ticket.

3 0

3 years ago

Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per

DochEvi [55]

first speed --- x mph

return speed -- x+16 mph

6/x + 6/(x+16) = 1

times each term by x(x+16)

6(x+16) + 6x = x(x+16)

x^2 + 4x - 96 = 0

(x-8)(x+12) = 0

x = 8 or x is a negative

her first speed was 8 mph

her return speed was 24 mph

check:

6/8 + 6/24 = 1 , that's good!

8 0

3 years ago