All categories

3 years ago

What is the inverse of the function f(x) = 2x – 10

Mathematics

2 answers:

BartSMP [9]3 years ago

6 0

Answer:

y = 1/2x +5

Step-by-step explanation:

change f(x) to y

y = 2x - 10

then switch x and y

x = 2y - 10

then solve for y

add 10 to both sides and divide both sides by 2

Ksenya-84 [330]3 years ago

6 0

Answer:

Step-by-step explanation:

One way to find the inverse is:

1. replace the symbol f(x) with y (for simplicy--stay tuned). Now you have

y = 2x -10

2. switch x and y. You get x = 2y - 10

3. Solve for y.

x + 10 = 2y

y = (x + 10)/2

4. Replace y with the symbol for the inverse function,

Another approach is to think about inverse operations in reverse order.

f(x): start with x

multiply by 2

subtract 10

Inverse: start with x

add 10 (addition is the inverse of subtraction)

divide by 2 (division is the inverse operation of multiplication)

You might be interested in

Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.

Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function f(x, y) for which

grad f(x, y) = F(x, y)

This amounts to solving for f such that

∂f/dx = x + 3

∂f/∂y = 6y + 3

Integrating both sides of the first equation with respect to x gives

f = 1/2 x ^2 + 3x + g(y)

Differentiating with respect to y gives

∂f/∂y = dg/dy = 6y + 3

Solving for g gives

g = ∫ (6y + 3) dy = 3y ^2 + 3y + C

and hence

f(x, y) = 1/2 x ^2 + 3x + 3y ^2 + 3y + C

(a) By the fundamental theorem, the integral of F along any path starting at the point P (1, 0) and ending at Q (3, 3) is

∫ F(x, y) • dr = f (3, 3) - f (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to P :

∫ F(x, y) • dr = f (1, 0) - f (0, 0) = 7/2 - 0 = 7/2

• From Q back to the origin:

∫ F(x, y) • dr = f (0, 0) - f (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

6 0

3 years ago

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

lora16 [44]

Answer:

<h2>not exist</h2>

Step-by-step explanation:

The coordinates of the intersection of the line are the solution of the system of equations.

$\underline{+\left\{\begin{array}{ccc}x-y=1\\y-x=1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=2\qquad\bold{FALSE}$

The system of equations has no solution. Therefore, the lines are parallel (the intersection does not exist).

5 0

3 years ago

Find the answer please

Oliga [24]

256. Since each side is congruent, the length equals 8. 8 times 8 equals 64. Divide it by 2 to find the area of the triangle. 64 divided by 2 equals 32. Since there are 8 congruent triangles, 32 x 8 equals 256.

6 0

2 years ago

Tamar has four more quarters than dimes. If he has a total of $1.70, how many quarters

erma4kov [3.2K]

<h3>Answers:</h3><h3>6 quarters</h3><h3>2 dimes</h3>

================================================

Work Shown:

d = number of dimes

q = number of quarters

q = d+4 since she has 4 more quarters than dimes

$1.70 = 170 cents

10d = value of all the dimes in cents

25q = value of all the quarters in cents

10d+25q = total value of all the coins in cents

10d+25q = 170

10d+25( q ) = 170

10d+25( d+4 ) = 170 .... plug in q = d+4

10d+25d+100 = 170 .... distribute

35d+100 = 170

35d = 170-100 ..... subtract 100 from both sides

35d = 70

d = 70/35 ... divide both sides by 35

d = 2

He has 2 dimes

q = d+4

q = 2+4

q = 6

He also has 6 quarters

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

Check:

1 dime = 10 cents

2 dimes = 20 cents ..... multiply both sides by 2

1 quarter = 25 cents

6 quarters = 150 cents ..... multiply both sides by 6

(2 dimes) + (6 quarters) = (20 cents) + (150 cents) = 170 cents

This confirms the answers.

5 0

3 years ago

A data analyst has spreadsheets numbered

algol [13]

Answer:

$\frac{2}{9}$

Step-by-step explanation:

${\textrm}{Total number of objects here} = 9$

(2 spreadsheets, 3 databases and 4 presentations,

${\textrm}({Total} = 2+3+4 = 9)$

${\textrm}{No. of databases with an odd number} = 2 {\textrm}{(databases with number 1 and 3})$

As not mentioned other wise equal chances of all the outcomes is assumed so, by the classical definition of probability,

P(The chosen item is a odd numbered database)

= $\frac{2}{9}$

8 0

2 years ago