Question

For given functions f and g, complete parts (a)-(h). For parts (a,d) also find the domain.

(a) find (f+g)(x)

(f+g)(x) = (simplify your answer)

Answer 1

`(f+g)(x)=(16x+9)/(9x-7)`

Explanation:

Given functions:

`f(x)=(7x+9)/(9x-7)`

`g(x)=(9x)/(9x-7)`

To find (f + g)(x), simply add the two functions f(x) and g(x).

As both functions have the same denominator, we can apply the fraction rule:

`\boxed{ (a)/(c)+(b)/(c)=(a+b)/(c)}`

Therefore:

`\begin{aligned}(f+g)(x)&=f(x)+g(x)\\\\&=(7x+9)/(9x-7)+(9x)/(9x-7)\\\\&=(7x+9+9x)/(9x-7)\\\\&=(16x+9)/(9x-7)\end{aligned}`