Step-by-step explanation:
We can observe from the table that the value of independent variable and then the values of function on that variable are given.
So,
<u>f(5) = 6</u>
As the value of function at x=5 is 6
<u>If f(x) = 4 then x = 7</u>
The value of function is 4 only on x=7 so the answer is x = 7
When the inverse is taken, the inputs become output and the outputs become inputs
![f^{-1}(6) = 5](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%205)
The value of inverse will be 5 because in original function 5 is input and 6 is output when this will be reversed for inverse, the output will be 5 for 6
Now,
Lastly
![if\ f^{-1}(x) = 7,\ then \x = 4](https://tex.z-dn.net/?f=if%5C%20f%5E%7B-1%7D%28x%29%20%3D%207%2C%5C%20then%20%5Cx%20%3D%204)
The reverse rule of input and output will be used. The reverse function will generate 7 at input 4.
First of all, we can observe that
![x^2-6x+9 = (x-3)^2](https://tex.z-dn.net/?f=x%5E2-6x%2B9%20%3D%20%28x-3%29%5E2)
So the expression becomes
![\dfrac{x^2-4}{\sqrt{(x-3)^2}} = \dfrac{x^2-4}{|x-3|}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2-4%7D%7B%5Csqrt%7B%28x-3%29%5E2%7D%7D%20%3D%20%5Cdfrac%7Bx%5E2-4%7D%7B%7Cx-3%7C%7D)
This means that the expression is defined for every ![x\neq 3](https://tex.z-dn.net/?f=x%5Cneq%203)
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
![x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2](https://tex.z-dn.net/?f=x%5E2-4%20%5Cgeq%200%20%5Ciff%20x%5Cleq%20-2%20%5Clor%20x%5Cgeq%202)
Since we can't accept 3 as an answer, the actual solution set is
![(-\infty,-2] \cup [2,3) \cup (3,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-2%5D%20%5Ccup%20%5B2%2C3%29%20%5Ccup%20%283%2C%5Cinfty%29)
Answer:
you get 8 oranges
Step-by-step explanation:
5 + 3 = 8 oranges
It should be a cylinder generated by the rotation. Take a piece of paper or book and rotate it with one edge as the center, and visualize what shape it makes. Doing something like this will be the best way to understand what shape it forms.
Answer:
1/2 of an answer is zero
Step-by-step explanation: