Suppose a horse is galloping at 19 mph toward a clown, and the clown is racing toward the horse on an ATV which can sustain a sp
1 answer:
Answer:
It will take 1.47 hours for the horse and clown to collide
Step-by-step explanation:
They are driving toward each other, in opposite directions.
So to find their speed of approximation, we add their speeds.
19 mph + 15 mph = 34 mph.
This means that each hour, they are 34 miles closer.
How long it takes for them to find each other if they are 50 miles apart?
1 hour - 34 miles
x hours - 50 miles
It will take 1.47 hours for the horse and clown to collide
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that is correct hmmmm, yes, I think the restriction is also correct, it has to be x > 0, because, the domain on the original, has a restriction of x⩾3, otherwise the radicand turns negative.
now, the graph of that original function is a parabola sideways opening to the right, if you include both sides of the vertex of the parabola, it will not pass the vertical-line-test and not be a function, but if you restrict it to only positive roots, so it'll only be on the 1st quadrant, then it functions ok.
that means, the range of the original function, has to stick to only 0 or positive root values, now, recall that the range of the original is the domain of the inverse. Therefore, the domain of the inverse, will have to stick to only 0 or positive values, since it's bound to the same restriction as the original's range.
notice the picture below of both, the dashed section is the positive range for each, if you include it, the original will fail the vertical-line-test, and the inverse will fail the horizontal-line-test.
recall that for a function to have an inverse, they both must pass the vertical and horizontal line test, or be a one-to-one functions.
