SOLUTION: 1) Given the function f:x=6X-(2/X), X>0, Find: a) F-1(inverse) b) f-1(-1) c) f-1(-4)

Algebra ->  Rational-functions -> SOLUTION: 1) Given the function f:x=6X-(2/X), X>0, Find: a) F-1(inverse) b) f-1(-1) c) f-1(-4)      Log On


   

Question 364470: 1) Given the function f:x=6X-(2/X), X>0, Find:
a) F-1(inverse)
b) f-1(-1)
c) f-1(-4)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=6x-2%2Fx
x=6y-2%2Fy
xy=6y%5E2-2
6y%5E2-xy=2
Complete the square in y.
6%28y%5E2-%28x%2F6%29y%29=2
6%28y%5E2-%28x%2F6%29y%2B%28x%5E2%2F144%29%29=2%2B6%28x%5E2%2F144%29
6%28y-x%2F12%29%5E2=2%2Bx%5E2%2F24
%28y-x%2F12%29%5E2=1%2F3%2Bx%5E2%2F144
y-x%2F12=0+%2B-+sqrt%281%2F3%2Bx%5E2%2F144%29
y=x%2F12+%2B-+sqrt%281%2F3%2Bx%5E2%2F144%29
highlight%28f%5E%28-1%29%28x%29=x%2F12+%2B-+sqrt%281%2F3%2Bx%5E2%2F144%29%29
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Use the inverse function and substitute x=-1 and x=-4 and solve for f%5E%28-1%29%28x%29.