Given the two functions f(x)and g(x)�‚0 for all x, explain how to find (f+g)(x),(f-g)(x),(f*g)(x), and (f�€g)(x).Demonstrate examples for all:

f(x)=(-x)/(6)-3(5+3x)/(8)-3x
f(0)=-15/8

you did not state g(x)

for (f+g)(x) just add up the two expression
for (f-g)(x) just subtract the two expression
for (f*g)(x) just multiply the two expressions

I don't know what operation (f€g)(x) is supposed to be

this question wants you to make up the functions of f(x) and g(x) to proform each expression

To find the values of (f+g)(x), (f-g)(x), (f*g)(x), and (f÷g)(x), you need to first have the function definitions for both f(x) and g(x). Once you have those, you can perform the respective operations on the functions.

1. (f+g)(x):
To find (f+g)(x), you simply add the two functions together by replacing f(x) and g(x) with their respective expressions. The resulting equation will be the sum of f(x) and g(x).
Example:
Let's say g(x) = 2x + 1.
(f+g)(x) = f(x) + g(x) = (-x)/(6) - (3(5+3x))/(8) - 3x + 2x + 1
Simplifying further, you would combine like terms and perform any necessary calculations.

2. (f-g)(x):
To find (f-g)(x), you subtract g(x) from f(x) by replacing f(x) and g(x) with their respective expressions.
Example:
Let's use the same g(x) as before.
(f-g)(x) = f(x) - g(x) = (-x)/(6) - (3(5+3x))/(8) - 3x - (2x + 1)
Simplifying further, you would combine like terms and perform any necessary calculations.

3. (f*g)(x):
To find (f*g)(x), you multiply f(x) and g(x) together by replacing f(x) and g(x) with their respective expressions.
Example:
Let's use the same g(x) as before.
(f*g)(x) = f(x) * g(x) = [(-x)/(6) - (3(5+3x))/(8) - 3x] * (2x + 1)
Simplifying further, you would distribute and combine like terms, then perform any necessary calculations.

4. (f÷g)(x):
To find (f÷g)(x), you divide f(x) by g(x) by replacing f(x) and g(x) with their respective expressions.
Example:
Let's use the same g(x) as before.
(f÷g)(x) = f(x) ÷ g(x) = [(-x)/(6) - (3(5+3x))/(8) - 3x] / (2x + 1)
Simplifying further, you would follow the rules of dividing fractions and perform any necessary calculations.

Since you've provided the function definition for f(x) and the value of f(0), you can plug in x = 0 to find f(0).
f(0) = [-0/(6) - (3(5+3(0)))/(8) - 3(0)]
Simplify to find the value of f(0).
f(0) = -15/8

Now you can use the given values of f(x) and g(x) to evaluate the functions (f+g)(x), (f-g)(x), (f*g)(x), and (f÷g)(x) using the explained steps above.