Question

F(x)=3 |x+4|-2
for what values of x does f(x)=19?

Answer 1

The values of x for which f(x) = 19 are x = 3 and x = -11. However, since the context implies that only values between 0 and 20 are considered, the only acceptable solution is x = 3.

Step-by-step explanation:

To find the values of x for which f(x) = 19, let's start by setting the function equal to 19:

3 |x+4| - 2 = 19.

First, add 2 to both sides of the equation to isolate the absolute value:

3 |x+4| = 21

Then, divide both sides by 3:

|x+4| = 7

Next, we solve for the two cases of the absolute value, for when (x+4) is positive and when it is negative:

x + 4 = 7 or x + 4 = -7

For x + 4 = 7, solving for x gives:

x = 3

For x + 4 = -7, solving for x gives:

x = -11

So, the values of x for which f(x) = 19 are x = 3 and x = -11.

Note that this solution assumes x can be any real number within the mentioned graph range (0 ≤ x ≤ 20). However, since x = -11 is not within this range, the only acceptable solution in this context is x = 3.