SOLUTION: Let �(x) = 3x2 � 2x and g(x) = x � 6. (f/g)(-1)= solve equations: (4x-3)^3/2=8 (-2-x)^0.5-x=2 I am a mom trying to help my daughter and I just don't get it!

Click here to see ALL problems on Rational-functions

Question 564236: Let �(x) = 3x2 � 2x and g(x) = x � 6.
(f/g)(-1)=
solve equations:
(4x-3)^3/2=8
(-2-x)^0.5-x=2
I am a mom trying to help my daughter and I just don't get it!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Let �(x) = 3x^2 � 2x and g(x) = x � 6.
--------------------------
(f/g)(-1)= = f(-1)/g(-1)
= [3(-1)^2-2(-1)]/[-1-6]
= [3*1+2]/[-7]
= -5/7
==============================
solve equations:
(4x-3)^3/2=8
(4x-3) = 8^(2/3)
(4x-3) = 2^2
4x-3 = 4
4x = 7
x = 7/4
==============================
(-2-x)^0.5-x = 2
---
sqrt(-2-x) = x +2
---
Square both sides:
-2-x = x^2+4x+4
x^2+5x+6 = 0
Factor:
(x+3)(x+2) = 0
x = -2 or x = -3
--
Checking those "answers":
(-2-x)^0.5-x = 2
Check x = -2:
(-2+2)^(0.5) +2 = 2
sqrt(0) + 2 = 2
2 = 2
----
Check x = -3
(-2+3)^(0.5) + 3 = 2
sqrt(1)+3 = 2
4 = 2
False
---
Only solution: x = -2
=============================
Cheers,
Stan H.
=============================