5. How does the length of the long leg compare to the length of the short leg?
1 answer:
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Answer with explanation:
Given the function f from R to
f:
To prove that the function is objective from R to
Proof:
When we prove the function is bijective then we proves that function is one-one and onto.
First we prove that function is one-one
Let
Cancel power on both side then we get
Hence, the function is one-one on domain [tex[(0,\infty)[/tex].
Now , we prove that function is onto function.
Let - f(x)=y
Then we get
The value of y is taken from
Therefore, we can find pre image for every value of y.
Hence, the function is onto function on domain
Therefore, the given is bijective function on
not on whole domain R .
Hence, proved.
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Answer:
maximum difference is 38 at x = -3
Step-by-step explanation:
This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.
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Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.
h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2
Then the derivative is ...
h'(x) = 3x² +4x -15 = (x +3)(3x -5)
This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.
The maximum difference between f(x) and g(x) is 38 at x = -3.
