Answer:
The two restrictions that we have for x are:
x < -2
x > -0.5
Explanation:
In part 3 we want to solve:
-5 < f(x) < 1
But we don't know the actual equation of f(x), we have only the graph, so let's work with that.
So with the graph, let's find the allowed values of x.
First, let's see the possible values of x such that:
-5 < f(x)
in the graph, we can see that:
f(-2) = -5
And as x decreases we will have:
f(x) > -5
So here we found one restriction for x, if we want:
f(x) > -5, then we must have x < - 2
Now let's find the other case, where:
f(x) > 1
Again, in the graph we can see that:
f(-0.5) = 1
And as x increases, the value of f(x) decreases.
so if x > -0.5
f(x) < 1.
Then we found another restriction for x:
x > -0.5
The two restrictions that we have for x are:
x < -2
x > -0.5
So if x is a value such that one of these two inequalities is true, then the inequality:
-5 < f(x) < 1
is true.