Question

G(x) = (simplify your answer. Use integers or fractions for any numbers in the expression)

Answer 1

g(x) = 1 - (16/5)x

Explanation:

f(x) = 3x + 5,

(f + g)(x) = 6 - (1/5)x

Now,

(f + g)(x) = f(x) + g(x)

g(x) = (f + g)(x) - f(x)

g(x) = 6 - (1/5)x - (3x + 5)

g(x) = 6 - (1/5)x - 3x - 5

g(x) = 6 - 5 - 3x - (1/5)x

g(x) = 1 - (16/5)x

Answer 2

`g(x)=1-(16)/(5)x`

Explanation:

Given functions:

`f(x)=3x+5`

`(f+g)(x)=6-(1)/(5)x`

The notation (f + g)(x) represents the sum of two functions f(x) and g(x) evaluated at a specific value of x. Therefore, to find g(x), we can subtract f(x) from (f + g)(x).

`\begin{aligned}g(x)&=(f+g)(x)-f(x)\\\\&=\left(6-(1)/(5)x\right)-(3x+5)\\\\&=6-(1)/(5)x-3x-5\\\\&=1-(1)/(5)x-(15)/(5)x\\\\&=1-(16)/(5)x\end{aligned}`

Therefore, function g(x) is:

`\large\boxed{g(x)=1-(16)/(5)x}`