The inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
To find the inverse of a function:
Interchange the f(x) and x
f(x) → x
x → f⁻¹(x)
Make the subject f(x);
Thus, the inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
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Answer:
The dilation on any point of the rectangle is 
.
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
![G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)]](https://tex.z-dn.net/?f=G%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2Bk%5Ccdot%20%5BG%28x%2Cy%29-O%28x%2Cy%29%5D)
(1)
Where:
- Coordinates of the point G, dimensionless.
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Coordinates of the point G', dimensionless.
If we know that 
, 
and 
, then scale factor is:
![(5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)]](https://tex.z-dn.net/?f=%285%2C-5%29%20%3D%20%280%2C0%29%20%2Bk%5Ccdot%20%5B%282%2C-2%29-%280%2C0%29%5D)
The dilation on any point of the rectangle is:
![P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Ccdot%20%5BP%28x%2Cy%29-%280%2C0%29%5D)
(2)
The dilation on any point of the rectangle is .
The answer is 3 because -3 times 2 is -6 , than 12 divided by -6 is -2 , than -2 plus 5 is 3 .
Given:
Number of miles covered = 
Length of each lap = 
of a mile.
To find:
The number of laps.
Solution:
We know that,
Therefore, Grayson ran 3 laps.
<u>Answer:
</u>
Johnny could play 
video games in 40 minutes.
<u>Explanation:</u>
Given:
Johnny played video games in an hour
= 
To Find:
Video games Jonny can play in 40 minutes
=?
Solution:
number of videos games Jonny can play in 1 hour = 
= 
And as 1 hour = 60 minutes ,
So number of videos games Jonny can play in 60 minutes =
=> Videos games Jonny can play in 1 minute =
=>
=> 
=> Videos games Jonny can play in 40 minute = 40 x Videos games Jonny can play in 1 minute
=> Videos games Jonny can play in 40 minute = 
=> 
=
Hence Johnny could play video games in 40 minutes.
