Go to desmos.com its a free graphing calculator site. type in (x+2)/(x-3)
it'll show you the graph
Answer:
![f^{-1}(x)=\sqrt[3]{x}-6](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D-6)
Step-by-step explanation:
![\sqrt[3]{x}=y+6](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%3Dy%2B6)
![\sqrt[3]{x}-6=y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D-6%3Dy)
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
