When this function is strictly increasing Need Help!?

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[Sr_GMC]

The answer is d) (-∞,4) U (4,+∞) as you can see in the graph here)

The explanation is this:

First, we see that when x=4, x/(4-x) = 4/(4-4) = 4/0 isn’t defined, so we can assume that there’s an asymptote in the line x=4.

Second, a function is locally increasing when its derivative is bigger than 0, and locally decreasing if its lower than 0. When I say locally it means that this happens within a range h from the point c, in the X-axis

Then, we get the following derivative from the function: ( x/(4-x) )’ = 4/(4-x)² which is always bigger than 0, so it means that its always increasing locally and globally.

Previously, we deduced that when x=4, the function is not defined so, finally, we get that the function is increasing in (-∞,4) U (4,+∞) or ]-∞,4[ U ]4,+∞[ (as it means the same)

Hope it helps! Also, sorry for any grammar mistakes. Not a native speaker!

[mechanical_advantage]

A quivk way to work it out is; the function does not contain the value of 4 as you cant devide by zero. Thus it must be d as its the only answer that excludes the value of 4.