If (f + g)(x) = 3x² + 2x - 1 and g(x) = 2x - 2, what is f(x)?

Solution:

Given: (f + g)(x) = 3x² + 2x - 1 and g(x) = 2x - 2

From the composite functions

(f + g)(x) = g(x) + f(x)

Substituting the values

3x² + 2x - 1 = 2x - 2 + f (x)

By further calculation,

f(x) = (3x² + 2x - 1) - (2x - 2)

So we get

f(x) = 3x² + 2x - 1 - 2x + 2

f(x) = 3x² + 1

Therefore, f(x) = 3x² + 1.

If (f + g)(x) = 3x² + 2x - 1 and g(x) = 2x - 2, what is f(x)?

Summary:

If (f + g)(x) = 3x² + 2x - 1 and g(x) = 2x - 2, then the value of f(x) is 3x² + 1.