Question

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let f(x)=3x + 4 and g(x)=2x - 5. find (f + g)(x), (f - g)(x), (fg)(x), and \\(\left(\frac{f}{g}\
ight)(x)\\). give the domain of each.
(f + g)(x) = 5x - 1 (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 that \(f(x) = 3x + 4\) and \(g(x)=2x - 5\). So, substitute these into the formula:
\((f - g)(x)=(3x + 4)-(2x - 5)\)

Step3: Simplify the expression

First, distribute the negative sign to the terms inside the parentheses:
\((f - g)(x)=3x + 4-2x + 5\)
Then, combine like - terms:
For the \(x\) - terms: \(3x-2x=x\)
For the constant terms: \(4 + 5=9\)
So, \((f - g)(x)=x + 9\)

Answer:

\(x + 9\)