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) = 9x - 2 (simplify your answer.)

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

Explanation:

Step1: Recall the formula for (f - g)(x)

The formula for the difference of two functions is \((f - g)(x)=f(x)-g(x)\).

Step2: Substitute the given functions

We know \(f(x) = 7x + 5\) and \(g(x)=2x - 7\). So, \((f - g)(x)=(7x + 5)-(2x - 7)\).

Step3: Simplify the expression

Remove the parentheses: \(7x+5 - 2x + 7\). Combine like terms: \((7x-2x)+(5 + 7)=5x+12\).

Answer:

\(5x + 12\)