Answer:
The inverse of the function is 
.
Step-by-step explanation:
The function provided is:
Let 
.
Then the value of <em>x</em> is:
For the inverse of the function, 
.
⇒
Compute the value of ![f[f^{-1}(x)]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D)
as follows:
![f[f^{-1}(x)]=f[\frac{x-5}{3}]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Df%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D)
![=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x](https://tex.z-dn.net/?f=%3D3%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D%2B5%5C%5C%5C%5C%3Dx-5%2B5%5C%5C%5C%5C%3Dx)
Hence proved that ![f[f^{-1}(x)]=x](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Dx)
.
Compute the value of ![f^{-1}[f(x)]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D)
as follows:
![f^{-1}[f(x)]=f^{-1}[3x+5]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Df%5E%7B-1%7D%5B3x%2B5%5D)
Hence proved that ![f^{-1}[f(x)]=x](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Dx)
.
The answer is 10. Hope I helped
Answer:
8. 24
9.55.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
The answer would be= 5.2857142857
