Question

Given f(x)=3x+1 and (f+g)(x)=6-1/2x, find the function g.

Answer 1

The questions have gotten more difficult as if this site is trying to do a test on the level of math a person knows so that they can give you that level everytime they use this site, and then sell it to other math website services who pay top dollar for it.

Step-by-step explanation:

Maybe if you keep the easy math questions going, you might get answers to them.

Answer 2

The function g(x) is g(x) =
`-(1)/(2)x - 5`.

Step-by-step explanation:

To find the function g(x), we'll use the given information that (f+g)(x) = 6 -
`(1)/(2)x\)` and f(x) = 3x + 1. The expression (f+g)(x) represents the sum of the functions f(x) and g(x).

Start by substituting the expression for f(x) into the sum:

(f+g)(x) = f(x) + g(x) =
`6 - (1)/(2)x\)`.

Replace f(x) with (3x + 1): 3x + 1 + g(x) = 6 -
`(1)/(2)x`.

Now, isolate g(x) by moving the terms involving g(x) to one side: g(x) = 6 -
`(1)/(2)x` - 3x - 1.

Combine like terms and simplify: g(x) =
`-(1)/(2)x` - 3x + 6 - 1.

Further simplify to obtain the final answer: g(x) =
`-(1)/(2)x` - 5.

In summary, the function g(x) is found by subtracting the expression for f(x) from the sum given in the problem. The steps involve substituting the known expression for f(x), isolating the terms involving g(x), and simplifying the result to obtain the final function for g(x), which is g(x) = -
`(1)/(2)x`- 5.