What is the math problem??
Answer:
a) f(x) = x^2
b) f(x) = x
c) any pair of numbers
Step-by-step explanation:
HI!
a)
an example of this kind of function is f(x) = x^2 because
f(x+h) = (x+h)^2 = x^2 + h^2 + 2 xh = f(x) + f(h) + 2xh
teherfore
f(x+h) ≠ f(x) + f(h)
other example is f(x) = x^n with n a whole number different than one
e.g.
f(x)=x^3
f(x+h) = (x+h)^3 = x^3 + h^3 + 3(x^2 h + x h^2) ≠ x^3 + h^3 = f(x) + f(h)
b)
f(x) = x is a function that actually behaves as indicated
f(x+h) = x + h = f(x) + f(h)
others examples of this kind of fucntion are given by multiplying x by any number:
f(x) = ax; f(x+h) = a(x+h) = ax + ah = f(x) + f(h)
c)
Any pair of numbers will make f(x+h) = f(x) + f(h), as mentioned in the previous section
lest consider 10 and 5
f(10+5) = 2 *(10+5) = 2*15 = 30
f(10) = 2*10 = 20
f(5) = 2*5 = 10
f(10) + f(5) = 20+10 = 30 = f(10+5)
Answer:
Entries of I^k are are also identity elements.
Step-by-step explanation:
a) For the 2×2 identity matrix I, show that I² =I
![I^{2}=\left[\begin{array}{cc}1&0\\0&1\end{array}\right] \times \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\\\=\left[\begin{array}{cc}1\times 1+0\times 0&1\times 0+0\times 1\\0\times 1+1\times 0&0\times 0+1\times1\end{array}\right] \\\\=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ctimes%201%2B0%5Ctimes%200%261%5Ctimes%200%2B0%5Ctimes%201%5C%5C0%5Ctimes%201%2B1%5Ctimes%200%260%5Ctimes%200%2B1%5Ctimes1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Hence proved I² =I
b) For the n×n identity matrix I, show that I² =I
n×n identity matrix is as shown in figure
Elements of identity matrix are
As square of 1 is equal to 1 so for n×n identity matrix I, I² =I
(c) what do you think the enteries of Ik are?
As mentioned above
Any power of 1 is equal to 1 so kth power of 1 is also 1. According to this Ik=I
Answer:
Cool!
Step-by-step explanation:
Answer:
Your answer is 7.5 loaves were baked that morning.
Step-by-step explanation:
To find the percent of a number, you drop the percent sign, and move the decimal 2 places to the left. Then you multiply that by the other number.
Hope this helps!
Let me know if you still don't understand!
~Courtney
