Question

() = 2|x + 61 - 4, for what values of xis x) = 6?

Given the function
=-1, x= 11
O x=-1,*=-11
x=14, x=-26
x = 26, = -14

Answer 1

`x = - 1\: or \: x = - 11`

Explanation:

The given function is

`f(x) = 2 |x + 6| - 4`

We want to find the value of x, for which f(x) =6.

Let use equate the function to 6 and solve for x.

`2 |x + 6| - 4 = 6`

Add 4 to both sides to get:

`2 |x + 6| = 6 + 4 \\ 2 |x + 6| = 10`

Divide through by 2 to get:

`|x + 6| = 5`

Use the absolute value function definition to get:

`x + 6 = 5 \: or \: x + 6= - 5`

Subbtract 6 from both sides to get:

`x = 5 - 6\: or \: x = - 5 - 6`

`x = - 1 \: or \: x = - 11`