Answer:
![(f o g)(x) = 3x + \frac{2}{3}](https://tex.z-dn.net/?f=%28f%20o%20g%29%28x%29%20%3D%203x%20%2B%20%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
We have the function
and we have the function
. We want to find g(x) composed with f(x)
Then, the function (f o g)(x) is the same since f(g(x))
That is, you must do x = g(x) and then enter g(x) into the function f(x).
![f(g(x)) = (g(x)) -\frac{1}{3}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%28g%28x%29%29%20-%5Cfrac%7B1%7D%7B3%7D)
![f(g(x)) = (3x + 1) -\frac{1}{3}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%283x%20%2B%201%29%20-%5Cfrac%7B1%7D%7B3%7D)
Simplifying, we obtain:
![(f o g)(x) = 3x + 1 -\frac{1}{3}\\\\(f o g)(x) = 3x + \frac{2}{3}](https://tex.z-dn.net/?f=%28f%20o%20g%29%28x%29%20%3D%203x%20%2B%201%20-%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%28f%20o%20g%29%28x%29%20%3D%203x%20%2B%20%5Cfrac%7B2%7D%7B3%7D)
Finally. The composite function is:
![(f o g)(x) = 3x + \frac{2}{3}](https://tex.z-dn.net/?f=%28f%20o%20g%29%28x%29%20%3D%203x%20%2B%20%5Cfrac%7B2%7D%7B3%7D)
Answer:
f(2)= -4
Step-by-step explanation:
f(x)= -x^3 + 6x - 7
f(2) = -2^3 + 6*2 - 7
f(2)= -8 +12 -7
f(2)= 3-7
f(2)= -4
Answer:
Infinite solutions
Step-by-step explanation:
2x−7y=12 (1)
−x+3.5y=−6 (2)
(2) x = 3.5y + 6
(1) 2(3.5y+6) - 7y = 12
7y + 12 - 7y = 12
12 = 12 (a true statement)
Since the variable got eliminated and we got a true statement, the system has infinitely many solutions.
One of the solutions:
(6,0)
Answer:
maybee if you woudl actually type the problem down instead of screenshotting it some people may actually be able to see it and actually answer the problem
Step-by-step explanation:
By substitution,
![g(2)=6.1g(1)](https://tex.z-dn.net/?f=g%282%29%3D6.1g%281%29)
![g(3)=6.1g(2)=6.1^2g(1)](https://tex.z-dn.net/?f=g%283%29%3D6.1g%282%29%3D6.1%5E2g%281%29)
![g(4)=6.1g(3)=6.1^3g(1)](https://tex.z-dn.net/?f=g%284%29%3D6.1g%283%29%3D6.1%5E3g%281%29)
and so on, so that
[tex]g(n)=6.1^{n-1}g(1)=2.7\cdot6.1^{n-1}