# Let f(x) = 3x^{2} + x − 3 and g(x) = x^{2} − 5x + 1. Find f(x) − g(x).

The relationship between independent and dependent variable is defined by the function. It is denoted by f(x).

## Answer: The value of f(x) - g(x) is 2x^{2} + 6x − 4.

Let's find f(x) − g(x).

**Explanation:**

We know that (f - g)(x) = f(x) - g(x).

The domain of f(x) - g(x) consists of the numbers x that are in the domain of f and the domain of g.

⇒ f(x) - g(x) = (3x^{2} + x − 3) - (x^{2} − 5x + 1)

⇒ f(x) - g(x) = 3x^{2} + x − 3 - x^{2} + 5x - 1

⇒ f (x) - g (x) = 2x^{2} + 6x − 4