The given function is greater than or equal to 0 for the interval given as follows:
{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.
<h3>When a function is positive and when it is negative?</h3>
- A function is positive when it is above the x-axis.
- A function is negative when it is below the x-axis.
For this problem, with a closed interval, we have that the function is above for:
x ≤ -3, -1 ≤ x ≤ 0, x ≥ 2.
Hence the interval notation is:
{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.
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ANSWER

EXPLANATION
The given quadratic trinomial is

Comparing to the general quadratic trinomial:

We have a=1, b=10 and c=-8

The factors of -24 that adds up to 10 are -2 and 12.
We split the middle term to obtain;

Factor;

Factor further;

The last option is correct.
F(x) = 2x + 1
To find the inverse of a function you just need to switch the x by y or vice-versa:
-> y = 2x + 1
-> x = 2y + 1
After that you isolate the y again:
-> 2y = x - 1
-> y = (x-1)/2
-> f^-1 (x) = (x-1)/2
Answer: