Question

Ok I got another one I can figure out
The one-to-one function f is defined by f(x)=(4x-1)/(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.

Answer 1

f(x)=(4x-1)/(x+7)
y = (4x-1)/(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?

Answer 2

I don't know if this is right but this is what I came up with.

f^-1=(-7x+1)/(x-4)
domain f(^-1)=(-inf,-7)U(-7,inf)
range f(^-1)=(-inf,4)U(4,inf)

Let me know if it looks right. Thanks