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3 years ago

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

Mathematics

2 answers:

adoni [48]3 years ago

8 0

$f(x)=2x+1\\\\y=2x+1\\2x=y-1\\x=\dfrac{y-1}{2}\\\\f^{-1}(x)=\dfrac{x-1}{2}$

hodyreva [135]3 years ago

4 0

Answer:

The inverse f-1(x) = ( x - 2) / 2.

Step-by-step explanation:

Let 2x + 1 = y

Now find x in terms of y:

2x = y - 1

x = (y - 1) / 2

Replace the x by the inverse f-1(x) and the y by x, so we have:

f-1(x) = ( x - 2) / 2.

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Solve the quadratic equation by completing the square.<br> x^2+12x+52=0

White raven [17]

Answer:

(x + 6)² + 16 = 0

Step-by-step explanation:

To complete the square we will first need to get our equation to look like: x² + bx = c

Here we have x² + bx + c = 0 → x² + 12x + 52 = 0

First we need to subtract our c, in this case 52, from both sides to get x² + 12x = -52
We then need to add $(\frac{b}{2} )^{2}$ to both sides of the equation
Here our b value is 12, so plugging this into our formula we get $(\frac{12}{2} )^{2} =(6)^{2} =36$
Adding 36 to both sides our equation becomes: x² + 12x + 36 = -52 + 36
Then combining like terms on the right side we get x² + 12x + 36 = -16
Now making our left side of the equation into a perfect square we get: (x + 6)² = -16
Finally adding the 16 to both sides of the equation we get: (x + 6)² + 16 = 0

6 0

3 years ago

Find the x and y for numbers 2 and. 3 thank you

OLEGan [10]

Answer:

(0, 4 ) and (2, - 4 )

Step-by-step explanation:

(2)

3x + 4y = 16 → (1)

- 3x + 2y = 8 → (2)

Adding (1) and (2) term by term will eliminate the x- term

0 + 6y = 24

6y = 24 ( divide both sides by 6 )

y = 4

Substitute y = 4 into either of the 2 equations and solve for x

Substituting into (1)

3x + 4(4) = 16

3x + 16 = 16 ( subtract 16 from both sides )

3x = 0 , then

x = 0

solution is (0, 4 )

(3)

2x - 4y = 20 → (1)

5x + 4y = - 6 → (2)

Adding (1) and (2) term by term will eliminate the y- term

7x + 0 = 14

7x = 14 ( divide both sides by 7 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (2)

5(2) + 4y = - 6

10 + 4y = - 6 ( subtract 10 from both sides )

4y = - 16 ( divide both sides by 4 )

y = - 4

solution is (2, - 4 )

5 0

3 years ago

What would the equation be for this table? (y=kx) Answer must be in y=kx form *

MakcuM [25]

Answer:

The answer is; M=9H

M=Money

H=Hours

Step-by-step explanation:

5 0

3 years ago

A regular octagon with sides of length 7 and an apothem of length 10.49 has an area of how many square units

Ray Of Light [21]

Answer:

The area of the regular octagon is $293.72\ units^{2}$

Step-by-step explanation:

we know that

The area of the regular polygon is equal to

$A=\frac{1}{2}Pa$

where

P is the perimeter of the regular polygon

a is the apothem

<em>Find the perimeter P</em>

$P=8(7)=56\ units$

Find the area

$A=\frac{1}{2}(56)(10.49)=293.72\ units^{2}$

6 0

3 years ago

(2x-3)(3x-4) Express as a trinomial

crimeas [40]

Answer:

6x² - 17x + 12

Step-by-step explanation:

Given

(2x - 3)(3x - 4)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(3x - 4) - 3(3x - 4) ← distribute both parenthesis

= 6x² - 8x - 9x + 12 ← collect like terms

= 6x² - 17x + 12

8 0

2 years ago