Question

For the function f(x) = x², what is f(x) + f(x) + f(x)?

A. 3f(x)
B. 3f(x) = 3x²
C. Evaluate 3f(2) = 12
D. g(x) = x - 6, if the opposite of g(x) is -g(x), then -g(x) = -x + 6, g(x) + (-g(x)) = 0

Answer 1

Adding the function f(x) = x² three times results in 3f(x), which simplifies to 3x². For the function g(x) = x - 6, its opposite is -g(x) = -x + 6, and when these are added together, they cancel out to give zero.

Step-by-step explanation:

The student's question is asking us to add the function f(x) = x² to itself three times and to also consider the function g(x) and its negative. When we add f(x) to itself three times, we get f(x) + f(x) + f(x), which simplifies to 3f(x). This is because adding the same function to itself multiple times is equivalent to multiplying the function by the number of times it is being added. Therefore, 3f(x) is the same as 3x².

In the case of g(x), we have g(x) = x - 6, and thus its opposite -g(x) is -x + 6. When we add g(x) and -g(x) together, the result is zero since each term in g(x) is cancelled by its corresponding term in -g(x), following the property that A + B = B + A and that summed opposites result in zero.