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MAVERICK [17]
2 years ago
10

Find the inverse

}^{3x - 1} " alt="f(x)={e}^{3x - 1} " align="absmiddle" class="latex-formula">
Tank you for your support ​
Mathematics
1 answer:
FromTheMoon [43]2 years ago
8 0

Answer:

f^{-1}(x)=\dfrac{1}{3}(\ln x +1)

Step-by-step explanation:

Given function:

f(x)=e^{3x-1}

Replace f(x) with y:

\implies y=e^{3x-1}

Take natural logs of both sides:

\implies \ln y = \ln e^{3x-1}

Apply the Power Log Law   \ln x^n=n\ln x :

\implies \ln y = (3x-1)\ln e

As \ln e=1 then:

\implies \ln y = 3x-1

Rearrange to make x the subject:

\implies 3x=\ln y +1

\implies x=\dfrac{1}{3}(\ln y +1)

Swap x for f^{-1}(x)  and y for x:

\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)

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What is the sales tax rate if a $7,190 purchase will have $568.01 of sales tax added to it?
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7.9%

Step-by-step explanation:

568.01/7190=0.079=7.9%

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3 years ago
#1. 10, 13, 16, 19, ... O y = 3 + 10x y = 10 + 3x O y = 3 + 7x O y = 7+ 3x<br> it's algebra ​
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5=7

Step-by-step explanation:

6 0
3 years ago
M3L3
eduard

The area of the David's pantry = 10 square feet.

The length of the pantry = 5 feet.

<h3>Define the term area of the rectangle?</h3>
  • The territory inhabited by a rectangle inside its 4 sides or limits is known as its area.
  • The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.

For the given question.

  • David's kitchen is 60 square feet in size.
  • The kitchen is six times the size of the living room.

Thus,

Area of kitchen  = 6 x area of the pantry

60 = 6 x area of the pantry

area of the pantry = 60 / 6 = 10 square feet.

Area of the pantry = length x breadth

10 = length x 2

length = 10/2 = 5 feet.

Thus, the length of the pantry is found as the 5 feet.

To know more about the area of the rectangle, here

brainly.com/question/16239445

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6 0
10 months ago
The points (4, 9) and (0, 0) fall on a particular line. What is its equation in slope-intercept form?
Nikolay [14]

Answer:

The equation of the line would be y = 4/9x

Step-by-step explanation:

In order to find the equation, we first need to find the slope. We can do this by using the slope equation with the points.

m(slope) = (y2 - y1)/(x2 - x1)

m = (9 - 0)/(4 - 0)

m = 9/4

Now that we have this, we can use point-slope form along with one of the points to get the equation.

y - y1 = m(x -x1)

y - 0 = 4/9(x - 0)

y = 4/9x

5 0
3 years ago
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