Question

what is $(f - g)(x)$?
$f(x) = 5x + 2$
$g(x) = -2x$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of \((f - g)(x)\)

The difference of two functions \(f(x)\) and \(g(x)\) is defined as \((f - g)(x)=f(x)-g(x)\).
Given \(f(x) = 5x + 2\) and \(g(x)=-2x\), we substitute these into the formula: \((f - g)(x)=(5x + 2)-(-2x)\)

Step2: Simplify the expression

We know that subtracting a negative number is the same as adding its positive counterpart. So, \((5x + 2)-(-2x)=5x + 2+2x\)
Now, combine like terms. The like terms here are \(5x\) and \(2x\). Combining them gives \(5x+2x = 7x\)
So the simplified expression is \(7x + 2\)

Answer:

\(7x + 2\)