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

Answer:

There are no x-values that gives such result.

Step-by-step 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 $x$

$6-1=-0.5|2x+2|\\5=-0.5|2x+2|\\-\frac{5}{0.5}=|2x+2|\\ |2x+2|=-10$

There are two ways

$2x+2=-10$ and $2x+2=10$

The first solution is

$2x=-10-2\\x=\frac{-12}{2}\\ x=-6$

The second solution is

$2x=10-2\\x=\frac{8}{2}\\ x=4$

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.