Answer:
![f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = \frac{1}{20} x + \frac{1}{5} \\ substitute \: f {}^{ - 1} (x) \: for \: y \\ f {}^{ - 1} (x) = \frac{1}{20} x + \frac{1}{5}](https://tex.z-dn.net/?f=f%28x%29%20%3D%2020x%20-%204%20%5C%5C%20substitute%20%5C%3A%20y%20%5C%3A%20for%20%5C%3A%20f%28x%29%20%5C%5C%20y%20%3D%2020x%20-%204%20%5C%5C%20interchange%20%5C%3A%20x%20%5C%3A%20and%20%5C%3A%20y%20%5C%5C%20x%20%3D%2020y%20-%204%20%5C%5C%20swap%20%5C%3A%20the%20%5C%3A%20sides%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20equation%20%5C%5C%2020y%20-%204%20%3D%20x%20%5C%5C%20move%20%5C%3A%20the%20%5C%3A%20constant%20%5C%3A%20to%20%5C%3A%20the%20%5C%3A%20right%20%5C%3A%20hand%20%5C%5C%2020y%20%3D%20x%20%2B%204%20%20%5C%5C%20divide%20%5C%3A%20both%20%5C%3A%20sides%20%5C%3A%20by%20%5C%3A%2020%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B1%7D%7B20%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20%20%5C%5C%20substitute%20%5C%3A%20f%20%7B%7D%5E%7B%20-%201%7D%20%28x%29%20%5C%3A%20for%20%5C%3A%20y%20%5C%5C%20f%20%7B%7D%5E%7B%20-%201%7D%20%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B20%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20)
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
Thus, domain of f(x): x∈R = range of f¯¹(x)
and range of f(x): x∈R =domain of f¯¹(x)
Answer:
Step-by-step explanation:
$62.50 $35.00/ $3.50 = 10
-$27.50 x=10
-------------
$35.00
Matteo can buy a maximum of 10 socks.
Answer:
- The total Minutes of the tasks involving animals.-D+F (Dog and fish)
- The total Minutes of the tasks not involving animals.-G (Garden)
- The total Minutes of the Inside tasks.-F (Fish)
- The total Minutes of the Outside tasks.-G+D (Garden and Dog)
Step-by-step explanation:
Given that:
- D = number of minutes it takes to walk his dog
- G = number of minutes it takes to water the garden; and
- F = number of minutes it takes to feed his fish
We want to match the given situations to its respective expressions:
Situation
- The total Minutes of the Inside tasks.
- The total Minutes of the Outside tasks.
- The total Minutes of the tasks involving animals.
- The total Minutes of the tasks not involving animals.
Expression
- D+F
- G+D
- G
- F
The match of the situation and respective expressions are:
- The total Minutes of the tasks involving animals.-D+F (Dog and fish)
- The total Minutes of the tasks not involving animals.-G (Garden)
- The total Minutes of the Inside tasks.-F (Fish)
- The total Minutes of the Outside tasks.-G+D (Garden and Dog)