Answer:
The proof is shown in the explanation below.
Step-by-step explanation:
Analysis:
The proof by induction focuses on n. In this case, let n = 1, and 
will be a linear operator since 
The exercise will show that 
is a linear operator on V and that 
is also a linear operator on V. This, follows that:
Answer:
Here we have the domain:
D = 0 < x < 1
And we want to find the range in that domain for:
1) y = f(x) = x
First, if the function is only increasing in the domain (like in this case) the minimum value in the range will match with the minimum in the domain (and the same for the maximums)
f(0) = 0 is the minimum in the range.
f(1) = 1 is the maximum in the range.
The range is:
0 < y < 1.
2) y = f(x) = 1/x.
In this case the function is strictly decreasing in the domain, then the minimum in the domain coincides with the maximum in the range, and the maximum in the domain coincides with the minimum in the range.
f(0) = 1/0 ---> ∞
f(1) = 1/1
Then the range is:
1 < x.
Notice that we do not have an upper bound.
3) y = f(x) = x^2
This function is strictly increasing, then:
f(0) = 0^2 = 0
f(1) = 1^2 = 1
the range is:
0 < y < 1
4) y = f(x) = x^3
This function is strictly increasing in the interval, then:
f(0) = 0^3 = 0
f(1) = 1^3 = 1
the range is:
0 < y < 1.
5) y = f(x) = √x
This function is well defined in the positive reals, and is strictly increasing in our domain, then:
f(0) = √0 = 0
f(1) = √1 =1
The range is:
0 < y < 1
Answer:
the answer is 2.34<2.43
Step-by-step explanation:
it is because 2.34 is less than 2.43
< means less than
> means greater than
= means equal to
B, 224in2
It may get tedious but just find the area of each face and write them down
Answer:
50
Step-by-step explanation:
10% of 100 is 10 so times it by 5
