Question

Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6?

Answer 1

There are no values. Given this graph, the maximum value is f(x) = 1

Answer 2

There are no x-values that gives such result.

Explanation:

The given function is

`f(x)=-0.5|2x+2|+1`

To find the values that gives
`f(x)=6`, we replace this

`6=-0.5|2x+2|+1`

Then, solve for
`x`

`6-1=-0.5|2x+2|\\5=-0.5|2x+2|\\-(5)/(0.5)=|2x+2|\\ |2x+2|=-10`

There are two ways

`2x+2=-10` and
`2x+2=10`

The first solution is

`2x=-10-2\\x=(-12)/(2)\\ x=-6`

The second solution is

`2x=10-2\\x=(8)/(2)\\ x=4`

Let's evalue the initial function for these values

`f(-6)=-0.5|2(-6)+2|+1=-0.5|-12+2|+1=-0.5(10)+1=-5+1=-4\\f(4)=-0.5|2(4)+2|+1=-0.5|8+2|+1=-0.5(10)+1=-5+1=-4`

Therefore, there are no x-values that gives such result.