Given the functions, f(x) = 5x2 - 3x + 1 and g(x) = 2x2 + x - 2, perform the indicated operation. When applicable, state the domain restriction.(f - g)(x)

To perform the operation (f - g)(x), we need to subtract the function g(x) from f(x).

f(x) = 5x^2 - 3x + 1 g(x) = 2x^2 + x - 2

Subtract g(x) from f(x):

(f - g)(x) = (5x^2 - 3x + 1) - (2x^2 + x - 2)

Distribute the negative sign to each term in the parentheses:

(f - g)(x) = 5x^2 - 3x + 1 - 2x^2 - x + 2

Combine like terms:

(f - g)(x) = (5x^2 - 2x^2) + (-3x - x) + (1 + 2)

This simplifies to:

(f - g)(x) = 3x^2 - 4x + 3

There are no domain restrictions for this function because you can plug any real number into the function and get a real number out.