(x) = x2. What is g(x)?

g(x) = (1/9)x^2

Step-by-step explanation:

Note that the two parabolas share a single vertex:  (0, 0).  Also note that g(x) is flatter than f(x), meaning that g(x) is formed by multiplying f(x) by a constant coefficient that is between 0 and 1.

If we model g(x) as g(x) = a(x^2) and then substitute 3 for x, then y at that point on the curve must be 1.  Thus:

1 = a(3^2), or 9a =1, or a = 1/9.  Thus, g(x) = (1/9)x^2.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3