SOLUTION: One-to-one function is h(x)=8x-3/3x+5. Find h^-1(x), where h^-1 is the inverse of h. Also state domain and range of h^-1 in interval notation.

Algebra ->  Rational-functions -> SOLUTION: One-to-one function is h(x)=8x-3/3x+5. Find h^-1(x), where h^-1 is the inverse of h. Also state domain and range of h^-1 in interval notation.       Log On


   

Question 1061291: One-to-one function is h(x)=8x-3/3x+5. Find h^-1(x), where h^-1 is the inverse of h. Also state domain and range of h^-1 in interval notation.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use x,y nomenclature.
y=%288x-3%29%2F%283x%2B5%29
Interchange x and y,
x=%288y-3%29%2F%283y%2B5%29
%283y%2B5%29x=8y-3
3xy%2B5x=8y-3
3xy-8y=-3-5x
%283x-8%29y=-3-5x
y=%283%2B5x%29%2F%288-3x%29
h%5E%28-1%29%28x%29=%283%2B5x%29%2F%288-3x%29
Domain is all x except,
8-3x=0
8=3x
x=8%2F3
Determine the range from the domain of the original function,
3x%2B5=0
3x=-5
x=-5%2F3
Since x=-5%2F3 is excluded from h domain, it is also excluded from the inverse's range.