Given the function f(x) = 3 |x – 2| + 6, for what values of x is f (x) = 18?

An expression with the absolute symbol is called an absolute function also called modulus value. It is defined as | x |.

Answer: The values of x for f (x) = 18 is 6 or - 2.

Let's find the values of x.

Explanation:

Given that f(x) = 3 |x – 2| + 6

To find the values of x put f (x) = 18

⇒ 3 |x – 2| + 6 = 18

By subtracting both the sides with 6, we get

⇒ 3 |x – 2| = 12

By dividing both the sides by 3, we get 

⇒ |x – 2| = 4

Absolute value function has two values x, solve for x.

⇒ |x – 2| = 4 will have two values of x

⇒ x – 2 = ± 4

⇒ x – 2 = 4 or x – 2 = - 4

⇒ x = 6 or - 2

You can check out Cuemath's online absolute value calculator.

Thus, the values of x for f (x) = 18 is 6 or - 2.