Question

Given the functions, f(x) = x 2 + x - 5 and g(x) = 4x 2 - 2x + 1, perform the indicated operation. When applicable, state the domain restriction. (f - g)(x)

Answer 1

Basically, this is asking you to subtract g(x) from f(x).

(f - g)(x) = (x^2 + x - 5) - (4x^2 - 2x + 1)

Distribute the negative sign into the second trinomial:

(f - g)(x) = x^2 + x - 5 - 4x^2 + 2x - 1

Combine like terms:

(f - g)(x) = -3x^2 + 3x - 6

There are no domain restrictions for this function. In other words, x can be any number without making the function undefined.