9514 1404 393
Answer:
see below
Step-by-step explanation:
We have elected to use a table, so that the rows and columns have labels that identify the table content. A matrix can be made from the data in the table.
For this case we have the following difference equation:

Applying separable variables we have:

Integrating both sides we have:

applying exponential to both sides:

For y (1) = 1 we have:

Thus, the particular solution is:

Whose domain is all real.
Answer: y = 0.2 * exp ((3/2) x ^ 2) Domain: all real numbers
You have a 1/2 chance of spinning an even number on the spinner, and a 1/2 chance of rolling an odd number on the die, 1/2 times 1/2 give you a 1/4 chance of doing both of those tasks.
(f∘g)(x) is equivalent to f(g(x)). We solve this problem just as we solve f(x). But since it asks us to find out f(g(x)), in f(x), each time we encounter x, we replace it with g(x).
In the above problem, f(x)=x+3.
Therefore, f(g(x))=g(x)+3.
⇒(f∘g)(x)=2x−7+3
⇒(f∘g)(x)=2x−4
Basically, write the g(x) equation where you see the x in the f(x) equation.
f∘g(x)=(g(x))+3 Replace g(x) with the equation
f∘g(x)=(2x−7)+3
f∘g(x)=2x−7+3 we just took away the parentheses
f∘g(x)=2x−4 Because the −7+3=4
This is it
g∘f(x) would be the other way around
g∘f(x)=2(x+3)−7
now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them.
g∘f(x)=2x+6−7
Next, +6−7=−1
g∘f(x)=2x−1
Its a lts easier than you think!
Hope this helped