SOLUTION: Given that F(x)= 7x-3/2x+5 is ONE-ONE find the following. a) D[f(x)] b) f^-1(x) c) R[f(x)]

Algebra ->  Real-numbers -> SOLUTION: Given that F(x)= 7x-3/2x+5 is ONE-ONE find the following. a) D[f(x)] b) f^-1(x) c) R[f(x)]      Log On


   

Question 1009324: Given that F(x)= 7x-3/2x+5 is ONE-ONE find the following.
a) D[f(x)]
b) f^-1(x)
c) R[f(x)]
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = (7x-3)/(2x+5)

domain: everything except x = -5/2

inverse: y = (7x-3)/(2x+5)
y(2x+5) = 7x-3
2xy + 5y = 7x - 3
2xy - 7x = -5y - 3
2x(y - 7/2) = -5y - 3
2x = (-5y-3)/(y - 7/2)

f^(-1)(x) = (-5x-3)/(2x-7)

range: everything except 7/2