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3 years ago

7

What is the inverse of the function f(x) = 2x + 1?

1 answer:

aliina [53]3 years ago

5 0

First, conceptually understand what an inverse function is, it makes solving it very intuitive. An inverse function is simply a function which has points (y,x) for every point (x,y) of the parent function. So you are essentially taking all points of the parent function and switching the x and y coordinates for each. Those switched coordinates are produced by the "inverse function".

Mathematically then, finding the inverse function is a matter of solving for x and then switching the variable labels. In this case:

y=2x+1 subtract 1 from both sides

y-1=2x divide both sides by 2

(y-1)/2=x now just switch the labels for the variables...

y=(x-1)/2 so

f^-1(x)=(x-1)/2 is the inverse of f(x)=2x+1

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The linear equation y = mx + b contains the point (4, -2) and is perpendicular to the

xenn [34]

A linear equation is represented as: $y = mx + b$ .

The equation of the line is: $y =3x - 14$

First, we calculate the slope (m) of $6x + 18y = 11$

Make y the subject

$18y = -6x + 11$

Divide by 18

$y = -\frac{1}{3}x + \frac{11}{18}$

In $y = mx + b$

$m \to$ slope

So, the slope of $y = -\frac{1}{3}x + \frac{11}{18}$ is:

$m = -\frac 13$

Since, the line is perpendicular to $6x + 18y = 11$

The slope of the line is:

$m_1 = -\frac{1}{m}$

So, we have:

$m_1 = -\frac{1}{-1/3}$

$m_1 = 3$

The line passes through (4,-2).

So, the equation is:

$y =m(x - x_1) + y_1$

This gives:

$y =3(x - 4) -2$

$y =3x - 12 -2$

$y =3x - 14$

Hence, the linear equation is:

$y =3x - 14$

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3 years ago

Heather paid $1,493.30 for a computer. If the price paid includes a 9% sales tax, which of the following equations can be used t

aliina [53]

A because x is the original price, so you multiply by the tax (9%) which would convert to 1.09 which you would multiply to the x

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3 years ago

4(-4x - 3) > 36 with the steps

Sergeu [11.5K]

Answer:

x < -3

Step-by-step explanation:

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

−4x−3> 36/4

Divide 36 by 4 to get 9.

−4x−3>9

Add 3 to both sides.

−4x>9+3

Add 9 and 3 to get 12.

−4x>12

Divide both sides by −4. Since −4 is negative, the inequality direction is changed.

x< 12/-4

Divide 12 by −4 to get −3.

x < -3

5 0

2 years ago

Read 2 more answers

In a triangle, one of the angle measures 70°

Tanya [424]

Answer:

the two angles are 55° each

Step-by-step explanation:

Let the two equal angles be y each

Therefore,

70° + y + y = 180°

Collect like terms

2y = 180 — 70

2y = 110

Divide both side by the coefficient of y i.e 2

y = 110/2

y = 55°

Therefore, the two angles are 55° each

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3 years ago

The speed of light is about 1.9 x 10^5 miles per second. It takes about 500 seconds for light to travel from the Sun to Earth.

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We are 93,000,000 miles away from the sun. The answer should be 9.3 x 10^7.

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