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posledela
3 years ago
11

What is the correct inverse function for f(x)=ln(3x)?

Mathematics
2 answers:
Maslowich3 years ago
5 0

Let y = f(x)

y = ln(3x)

Exchange place with x and y.

x = ln(3y)

Solve for y.

y = (e^x)/3

Replace y with the inverse notation.

f^(-1) x = (e^x)/3

Done.



aleksandrvk [35]3 years ago
4 0

Answer:

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

Step-by-step explanation:

f(x)= ln(3x)

First we replace f(x) with y

y=ln(3x)

Now , interchange the variables x  and y

x= ln(3y)

Solve the equation for y

We know ln has base 'e'

e^x = 3y

divide by 3 on both sides

y= \frac{e^x}{3}

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

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A particle decays at a rate of 0.45% annually. assume and initial amount of 300 mg. (
raketka [301]
The increase is an exponential increase in a multiplier
100%+0.45%=100.45% and as decimal 1.0045

Final Value = Initial Value × multiplier^{number of years}
Final value = 300(1.0045)^{60}
Final value = 393 mg (to the nearest whole number)

Half life = 0.5 years
Final value = 300(1.0045)^{0.5}=301 mg
6 0
3 years ago
LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE
Sidana [21]

Answer:

Segment EF: y = -x + 8

Segment BC: y = -x + 2

Step-by-step explanation:

Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.

Upon observing the given diagram, we can infer the following corresponding sides:

\displaystyle\mathsf{\overline{BC}\:\: and\:\:\overline{EF}}

\displaystyle\mathsf{\overline{BA}\:\: and\:\:\overline{ED}}

\displaystyle\mathsf{\overline{AC}\:\: and\:\:\overline{DF}}

We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.

<h2>Slope of Segment BC:</h2>

In order to solve for the slope of segment BC, we can use the following slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}  }

Use the following coordinates from the given diagram:

Point B:  (x₁, y₁) =  (-2, 4)

Point C:  (x₂, y₂) = ( 1,  1 )

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{1\:-\:4}{1\:-\:(-2)}\:=\:\frac{-3}{1\:+\:2}\:=\:\frac{-3}{3}\:=\:-1}

<h2>Slope of Segment EF:</h2>

Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:

Point E:  (x₁, y₁) =  (4, 4)

Point F:  (x₂, y₂) = (6, 2)

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{2\:-\:4}{6\:-\:4}\:=\:\frac{-2}{2}\:=\:-1}

Our calculations show that segment BC and EF have the same slope of -1.  In geometry, we know that two nonvertical lines are <u>parallel</u> if and only if they have the same slope.  

Since segments BC and EF have the same slope, then it means that  \displaystyle\mathsf{\overline{BC}\:\: | |\:\:\overline{EF}}.

<h2>Slope-intercept form:</h2><h3><u>Segment BC:</u></h3>

The <u>y-intercept</u> is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.

Using the slope of segment BC, m = -1, and the coordinates of point C, (1,  1), substitute these values into the <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>

y = mx + b

1 = -1( 1 ) + b

1 = -1 + b

Add 1 to both sides to isolate b:

1 + 1 = -1 + 1 + b

2 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.

Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:

⇒  y = -x + 2.

<h3><u /></h3><h3><u>Segment EF:</u></h3>

Using the slope of segment EF, <em>m</em> = -1, and the coordinates of point E, (4, 4), substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b. </em>

y = mx + b

4 = -1( 4 ) + b

4 = -4 + b

Add 4 to both sides to isolate b:

4 + 4 = -4 + 4 + b

8 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.

Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:

⇒  y = -x + 8.

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What is the solution, if any, to the inequality |3x|≥0?
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The inequality is all real numbers.

<h3>What is inequality?</h3>

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

|3x|≥0

3x = 0

Divide both sides of the equation by the coefficient of variable

x= 0/3

x=0 = RHS

Learn more about inequality here:

brainly.com/question/20383699

#SPJ1

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Answer:

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3 years ago
y-1/6x+5=0 Is this written in standard form if not then what is the equation in standard form. A.yes B.no;y=1/6x-5 C.x=-6y+30 D.
trasher [3.6K]

Answer:

Step-by-step explanation:

Not in standard form. The coefficients should be integers and the coefficient of x should be positive.

x+6y=30

Note that the choices given are not in standard form.

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