The answer is:
The inverse of a function is another function, , with the following property:
In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.
Think for example to a function that doubles the input, , and one that halves it: . Their composition is clearly the identity function , since you consider "twice the half of something", or "half the double of something".
In general, to invert a function , you have to solve the expression for , writing an expression like . If you manage to do so, then is the inverse of .
In your case, you have
Multiply both sides by to get
Square both sides to get
Finally, subtract 3 from both sides to get
Since the name of the variables doesn't really have a meaning, you can say that the inverse function is
As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain such that there exists . So, we need the range of .
We know that the range of is . When you transform it to you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times you affect both extrema of the range, turning it into , which you can simply write as
Answer:
Step-by-step explanation:
<h3>Part A</h3>
- The base is a rectangle hence the parallel cut produces the same shape.
<h3>Part B</h3>
- The cut diagonal to base will produce rectangle as the cross section still contains two pairs of parallel lines
There are 72 boys. 7:6 = 84:?, divide 84 by 7, you get 12. Multiply 6 by 12 to get the answer.
9514 1404 393
Answer:
A. √13
Step-by-step explanation:
You can make an educated guess and come to the right conclusion.
The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.
So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:
__
A -- between 3 and 4, the correct choice
B -- 3, too short
C -- 1.73, too short
D -- more than 4, too long
__
The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.
c = √(a^2 +b^2 -2ab·cos(C))
c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)
c = √13 . . . . . length of the side opposite the 60° angle
Answer:
2 coins
Step-by-step explanation: