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Fudgin [204]
3 years ago
5

How does one find the inverse function of f(x)=

le="\frac{1}{3x-1}" alt="\frac{1}{3x-1}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
lisabon 2012 [21]3 years ago
7 0

Answer:

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

Step-by-step explanation:

<u>The Inverse of a Function</u>

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

\displaystyle y=\frac{1}{3x-1}

* Solve the equation for x.

Multiply by 3x-1

y(3x-1)=1

Divide by y:

\displaystyle 3x-1=\frac{1}{y}

Sum 1:

\displaystyle 3x=\frac{1}{y}+1

Operate the right side:

\displaystyle 3x=\frac{1+y}{y}

Divide by 3:

\displaystyle x=\frac{1+y}{3y}

* Swap the variables:

\displaystyle y=\frac{1+x}{3x}

Write back into function form:

\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}

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Use the Midpoint formula


Under a radical it would be


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The down arrow is subscript -

So use the numbers from the two coordinates to plug in.

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3 years ago
What is the volume of the triangular prism below? 12 ft 7 ft 16 ft 5 ft​
Nina [5.8K]
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3 years ago
A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even e
snow_tiger [21]

Answer:

The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.

Step-by-step explanation:

Given :  A potato launched by a particular potato gun has a height described by  h ( t ) =-16 t^2+124 t+4.

To find : When is the potato 224 feet in the air?

Solution :

When the potato is 224 feet in the air i.e. h(t)=224

Substitute in the equation h ( t ) =-16 t^2+124 t+4,

224=-16 t^2+124 t+4

16t^2-124 t+220=0

4t^2-31t+55=0

Applying quadratic formula, x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here, a=4, b=-31 and c=55

t=\frac{-(-31)\pm\sqrt{(-31)^2-4(4)(55)}}{2(4)}

t=\frac{31\pm\sqrt{81}}{8}

t=\frac{31\pm9}{8}

t=\frac{31+9}{8},\frac{31-9}{8}

t=5,2.75

The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.

5 0
3 years ago
*WILLL GIVE BRAINIEST TO COORECT RESPONCE*<br> how do i do this?<br> what is the answer?
Sergio [31]

Answer:

line mo

Step-by-step explanation:

Because the triangle are congrument

RST and MNO are the triangle

RT is a line in the RST triqangle

it is equal to the MO line in MNO

3 0
2 years ago
How do I do this?need help​
Lelu [443]
I have no clue at all
8 0
2 years ago
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