Answer:
The expression for (g(x)) is (4x + 5).
Explanation:
To find the expression for (g(x)), we can use the given information about ((f+g)(x)) and (f(x)). Since ((f+g)(x) = 10x + 7) and (f(x) = 6x + 2), we can set up the following equation:
(f+g)(x) = f(x) + g(x) = 10x + 7
Now, substitute the expression for (f(x)) into the equation:
6x + 2 + g(x) = 10x + 7
Next, isolate (g(x)) by moving the terms without (g(x)) to the other side of the equation:
g(x) = (10x + 7) - (6x + 2)
Now, simplify:
g(x) = 10x + 7 - 6x - 2
Combine like terms:
g(x) = (10x - 6x) + (7 - 2)
g(x) = 4x + 5
So, the expression for (g(x)) is (4x + 5).