Answer:
Inverse of f(x)=-x^3-9 is ![f^{-1}(x)=\sqrt[3]{-x-9}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7B-x-9%7D)
Option B is correct option.
Step-by-step explanation:
We need to find inverse of 
For finding the inverse replace f(x) with y
Now, solve for x
Adding 9 on both sides
Multiply both sides by -1
Taking cube root on both sides:
![x^3=-y-9\\\sqrt[3]{x^3} =\sqrt[3]{-y-9} \\x=\sqrt[3]{-y-9}](https://tex.z-dn.net/?f=x%5E3%3D-y-9%5C%5C%5Csqrt%5B3%5D%7Bx%5E3%7D%20%3D%5Csqrt%5B3%5D%7B-y-9%7D%20%5C%5Cx%3D%5Csqrt%5B3%5D%7B-y-9%7D)
Now replace x with f^{-1}(x) and y with x
So, inverse of f(x)=-x^3-9 is
Option B is correct option.
Answer:
Let me tell you something you can really trust
Everybody's got a wicked side
I know you think that you could never be like us
Watch and learn so you can get it right
You need to drag your feet
You need to nod your head
You need to lean back
Slip through the cracks
You need to not care
Uh, you need to not stare
You need a whole lotta help
(You need to not be yourself)
Step-by-step explanation:
it is a song
Either way nothing can more can be done do this problem
Answer:
- shortest: 3 ft
- other: 4 ft
Step-by-step explanation:
The right triangle with hypotenuse 5 that has legs that differ by 1 is the 3-4-5 right triangle. The legs are 3 ft and 4 ft.
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<em>Alternate solution</em>
If you have never heard of a 3-4-5 right triangle, you can figure the leg lengths algebraically using the Pythagorean theorem. Let x represent the length of the "other" leg. Then the shortest is (x-1). The Pythagorean theorem tells you ...
5^2 = (x)^2 +(x -1)^2
25 = 2x^2 -2x +1
12 = x^2 -x = x(x -1)
Factors of 12 that differ by 1 are 3 and 4 or -3 and -4. We want x to be positive, so the value of interest is x=4
The "other" leg is 4 ft; the shortest leg is 3 ft.
