Question

I. For g(x) = x + 3 and f(x) = -x + 4, (g - f) = -2x + 1.

II. For g(x) = x^2 - 2 and h(x) = 2x + 5, g(-6) + h(-6) = 27.

Answer 1

For the first statement, (g - f) = -2x + 1, we subtract f(x) from g(x) and simplify the expression to get -2x + 1. For the second statement, we substitute the given values into g(-6) + h(-6) and simplify to get 27.

Step-by-step explanation:

For the first statement, (g - f) = -2x + 1, we subtract f(x) from g(x), which gives us (x + 3) - (-x + 4). Simplifying this expression, we get x + 3 + x - 4, which further simplifies to 2x - 1.

Therefore, (g - f) = -2x + 1, and this statement is true.

For the second statement, we need to substitute the given values into g(-6) + h(-6).

Substituting -6 into g(x) = x^2 - 2 gives us g(-6) = (-6)^2 - 2 = 36 - 2 = 34.

Substituting -6 into h(x) = 2x + 5 gives us h(-6) = 2(-6) + 5 = -12 + 5 = -7.

Therefore, g(-6) + h(-6) = 34 + (-7) = 27, and this statement is true.