Question

what is f(x) + f(x) + f(x)? 3f(x) =
evaluate 3f(2) =

g(x) = x - 6
if the opposite of g(x) is -g(x), then -g(x) =

g(x) + (-g(x)) =
options: 2g(x), -2g(x), 0

Explanation:

Step1: Recall the property of adding a function and its opposite

For any function \( g(x) \), when we add \( g(x) \) and \( -g(x) \), we use the property of addition of real numbers (or functions) where \( a + (-a)=0 \) for any real number \( a \). Here, let \( a = g(x) \), so \( g(x)+(-g(x))=g(x)-g(x) \).

Step2: Simplify the expression

\( g(x)-g(x) \) means subtracting the function \( g(x) \) from itself. For example, if \( g(x)=x - 6 \), then \( -g(x)=-x + 6 \), and \( g(x)+(-g(x))=(x - 6)+(-x + 6)=x - 6 - x + 6 \). Combining like terms, \( x - x=0 \) and \( -6 + 6=0 \), so the result is \( 0 \).

Answer:

\( 0 \)