Question

If f(x)= x²+ 2x - 6 and g(x)= 3x² - 5x - 7, find f(x)-g(x).

A) - 2x² - 3x + 1
B) -2x² + 7x + 1
C) - 2x² - 3x - 13
D) 4x² - 3x - 13

Answer 1

To find f(x) - g(x), subtract g(x) from f(x), distribute the minus sign, and combine like terms. The result is -2x² + 7x + 1, which corresponds to option B.

Step-by-step explanation:

To find the difference between the functions f(x) and g(x), you subtract the values of g(x) from f(x). Here are the steps:

1. Write down f(x): f(x) = x² + 2x - 6.
2. Write down g(x): g(x) = 3x² - 5x - 7.
3. Calculate f(x) - g(x): (x² + 2x - 6) - (3x² - 5x - 7).
4. Distribute the minus sign through g(x): x² + 2x - 6 - 3x² + 5x + 7.
5. Combine like terms: -2x² + 7x + 1.

The result is -2x² + 7x + 1, which matches option B.