Final answer:
To find x for which f(x)>9, solve the inequality f(x)>9 by splitting it into two cases and solving each case individually. The solutions are x > 0 or x < -12.
Step-by-step explanation:
To find the values of x for which f(x) > 9, we need to solve the inequality f(x) > 9. The function f(x) = 3 + |x + 6|. We can rewrite this inequality as 3 + |x + 6| > 9. Subtracting 3 from both sides gives |x + 6| > 6. Since the absolute value of a number is always greater than or equal to 0, we can split the inequality into two cases: x + 6 > 6 and x + 6 < -6.
In the first case, solving x + 6 > 6 gives x > 0.
In the second case, solving x + 6 < -6 gives x < -12.
Combining the solutions from both cases, we have x > 0 or x < -12.