Given:
The table of values for the function f(x).
To find:
The values
and
.
Solution:
From the given table, it is clear that the function f(x) is defined as:
![f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}](https://tex.z-dn.net/?f=f%28x%29%3D%5C%7B%28-14%2C11%29%2C%28-7%2C-12%29%2C%28-12%2C-5%29%2C%289%2C1%29%2C%2810%2C-2%29%2C%28-2%2C13%29%5C%7D)
We know that if (a,b) is in the function f(x), then (b,a) must be in the function
. So, the inverse function is defined as:
![f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5C%7B%2811%2C-14%29%2C%28-12%2C-7%29%2C%28-5%2C-12%29%2C%281%2C9%29%2C%28-2%2C10%29%2C%2813%2C-2%29%5C%7D)
And,
![f^{-1}(f(a))=f^{1}(b)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%28a%29%29%3Df%5E%7B1%7D%28b%29)
...(i)
Using (i), we get
![f^{-1}(f(3.14))=3.14](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%283.14%29%29%3D3.14)
Now,
![f(f(-7))=f(-12)](https://tex.z-dn.net/?f=f%28f%28-7%29%29%3Df%28-12%29)
![f(f(-7))=5](https://tex.z-dn.net/?f=f%28f%28-7%29%29%3D5)
Therefore, the required values are
and
.
Answer:
v = 55
Step-by-step explanation:
Plug in the values provided into the equation
v = u + at
v = 23 + 8 * 4
Solve
v = 23 + 8 * 4
v = 23 + 32
<u>v = 55</u>
Answer:
(11,-8)
Step-by-step explanation:
f(x-2) determines a horizontal translation 2 units to the right. Since (9,-8) is the point for f(x) then f(x-2) will be the point (11,-8) where 9 has moved two units to the right 11.
Yes they are. if you multiply numerator and denominator of 3/7 by 6, you get 18/42