Answer:
The answer is below
Step-by-step explanation:
A composite function is a function which is placed inside another function, this type of function can be calculated by substituting one function into another function.
If two functions g(x) and f(x) are inverses, then each will reverse the effect of the other. That is, (f○g)(x)=f(g(x))=x and (g○f)(x)=g(f(x))=x.
Given that F(x) =(x+4)/3 and g(x) = 3x – 4
a) (f o g)(x) = f[g(x)]
= f(3x - 4)
= [(3x - 4) + 4]/3
= [3x - 4 + 4]/3
= 3x / 3
= 3
b) (g o f)(x) = g[f(x)]
= g[(x + 4)/3]
= 3(x + 4)/3 - 4
= x + 4 - 4
= x
We can see that (f o g)(x) = (g o f)(x) = x. Hence the functions are inverse functions.
We want a solution in the form
with derivatives
Substituting and its derivatives into the ODE,
gives
Shift the index on the second sum to have it start at :
and take the first term out of the other two sums. Then we can consolidate the sums into one that starts at :
and so the coefficients in the series solution are given by the recurrence,
or more simply, for ,
Note the dependency between every other coefficient. Consider the two cases,
- If , where is an integer, then
and so on, with the general pattern
- If , then
and we would see that for all .
So we have
so that one solution is
and the other is
I've attached a plot of the exact and series solutions below with , , and to demonstrate that the series solution converges to the exact one.
Answer:
5y=7
y=7/5
Step-by-step explanation:
6x+6y=-6
6x+y=-3
eliminate the 6x
then subtract y from 6y
then subtract -3 from -6
6y-y=5y
-6-(-13)=7
5y=7
divide 5 from both sides
y=7/5
then you eliminate the y and do the same thing :)
x=-12/5
If I can round the Answer would be:
7^3÷5+6= 74.6
I will wait for your response if it is not correct comment so I can keep looking.