SOLUTION: Could someone help with this please? I have to find the inverse and graph the function and its inverse on the same coordinate plane. Y= (index 3 radicand x)/2

Algebra ->  Rational-functions -> SOLUTION: Could someone help with this please? I have to find the inverse and graph the function and its inverse on the same coordinate plane. Y= (index 3 radicand x)/2      Log On


   

Question 544732: Could someone help with this please? I have to find the inverse and graph the function and its inverse on the same coordinate plane.
Y= (index 3 radicand x)/2
Found 2 solutions by ankor@dixie-net.com, lwsshak3:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
We can write it:
Y = 3sqrt%28x%29%2F2
:
Find the inverse, swap x for y and solve for x
x = 3sqrt%28y%29%2F2
multiply both sides by 2
2x =3sqrt%28y%29
Cube both sides
(2x)^3 = y
we can also write it
y = 8x^3 is the inverse
:
The graph
+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+%28x%5E%281%2F3%29%29%2F2%2C+8x%5E3%29+
For some reason I could not make the negative portion of the original equation come up on this, plot these two equations on a graphing calc to see it.
y = (x^(1/3))/2
y = 8x^3

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find the inverse and graph the function and its inverse on the same coordinate plane.
Y= (index 3 radicand x)/2
**
y=x^(1/3)/2 (original function)
To find inverse interchange x & y, then solve for y
x=y^(1/3)/2
2x=y^(1/3)
cube both sides
y^-1=8x^3 (inverse)
see following graph as a visual check:
..
+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2Cx%5E%281%2F3%29%2F2%2C8x%5E3%29+
sorry, but graph of the original function was only shown for x>0.