Answer:
(f - g)(x) = -x² + 3x + 7 ⇒ D
Explanation:
In the expression x - a, you will subtract a from x
Let us solve the question using this fact
∵ f(x) = 3x + 1
∵ g(x) = x² - 6
→ We need to find (f - g)(x), which means subtract g from x
∵ (f - g)(x) = (3x + 1) - (x² - 6)
→ The negative sign before (x² - 6) will change their signs
∵ - (x² - 6) = -(x²) + -(-6)
→ Remember (-)(+) = - and (-)(-) = (+)
∴ - (x² - 6) = -x² + 6
→ Substitute it in (f - g)(x)
∴ (f - g)(x) = 3x + 1 - x² + 6
→ Add the like terms
∴ (f - g)(x) = 3x - x² + (1 + 6)
∴ (f - g)(x) = 3x - x² + 7
→ Re-arrange the terms from the greatest power of x
∴ (f - g)(x) = -x² + 3x + 7