Question

let f(x)=7x + 5 and g(x)=2x - 7. find (f + g)(x), (f - g)(x), (fg)(x), and \\(\left(\frac{f}{g}\
ight)(x)\\). give the domain of each.

\\((f + g)(x) = \square\\) (simplify your answer.)

Explanation:

Step1: Recall the definition of function addition

To find \((f + g)(x)\), we use the definition \((f + g)(x)=f(x)+g(x)\).
Given \(f(x) = 7x + 5\) and \(g(x)=2x - 7\), we substitute these into the formula: \((f + g)(x)=(7x + 5)+(2x - 7)\).

Step2: Combine like terms

First, remove the parentheses: \(7x+5 + 2x-7\).
Then, combine the \(x\)-terms: \(7x+2x=9x\).
Next, combine the constant terms: \(5 - 7=-2\).
So, \((f + g)(x)=9x-2\).

Answer:

\(9x - 2\)