finding the inverse

Question

Find the inverse of f(x) = (5x-3)/(2x-5)

Answer 1

 f(x) = (5x-3)/(2x-5)

 

ie. y = (5x-3)/(2x-5).

 

Now, the rule is relabel x and y as y & x, respectively, then solve this equation for y.  That answer will be f^-1  ("f inverse).

 

It's easy.  You'll have to multiply both sides of your new (switched) equation by the denominator, and then distribute, and then factor out y from various terms, and finally solve for that 'new' y.

 

If you have a textbook, consult it--there are examples!

Answer 2

hey Brooke

f(x)=(5x-3)/(2x-5)

 y=(5x-3)/(2x-5)

swap the rule of x and y

x=(5y-3)/(2y-5)

solve for y

2xy-5x=5y-3

2xy-5y=5x-3

(2x-5)y=5x-3

y=(5x-3) /(2x-5) 

oddly enough f inverse of f is itself :)