Algebra
posted by Rachal on .
Ok I got another one I can figure out
The onetoone function f is defined by f(x)=(4x1)/(x+7).
Find f^1, the inverse of f. Then, give the domain and range of f^1 using interval notation.
f^1(x)=
Domain (f^1)=
Range (f^1)=
Any help is greatly appreciated.

f(x)=(4x1)/(x+7)
y = (4x1)/(x+7)
Rewrite as:
y = (4x)/(x+7) 1/(x+7)
Multiply both sides by x+7:
(x + 7)y = 4x  1
Expand out terms of the left hand side:
xy + 7y = 4x  1
xy  4x = 7y  1
x(y  4) = 7y  1
Divide both sides by y  4:
x = (7y  1)/(y  4)
f^1 = (7x  1)/(x  4)
Can you do the domain and range now? 
I don't know if this is right but this is what I came up with.
f^1=(7x+1)/(x4)
domain f(^1)=(inf,7)U(7,inf)
range f(^1)=(inf,4)U(4,inf)
Let me know if it looks right. Thanks