SOLUTION: Find inverse of the following function: f(x)= (x² + 9)/(x - 5) x≠5

Algebra ->  Inverses -> SOLUTION: Find inverse of the following function: f(x)= (x² + 9)/(x - 5) x≠5      Log On


   

Question 1197463: Find inverse of the following function:
f(x)= (x² + 9)/(x - 5) x≠5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find inverse of the following function:

f%28x%29=+%28x%5E2%2B+9%29%2F%28x+-+5%29 x%3C%3E5

recall that f%28x%29=y

y=+%28x%5E2%2B+9%29%2F%28x+-+5%29 ........swap variables

x=+%28y%5E2%2B+9%29%2F%28y+-+5%29...........solve for y

x%28y+-+5%29=+y%5E2%2B+9

xy+-+5x=+y%5E2%2B+9

-5x-9=+y%5E2-xy...complete square on right side

-5x-9=+%28y%5E2-xy%2B%28x%2F2%29%5E2%29-%28x%2F2%29%5E2

-5x-9=+%28y-x%2F2%29%5E2-x%5E2%2F4

x%5E2%2F4-5x-9=+%28y-x%2F2%29%5E2

sqrt%28%28x%5E2+-+20+x+-+36%29%2F4+%29=+y-x%2F2

y=%281%2F2%29sqrt%28x%5E2+-+20+x+-+36%29%2Bx%2F2


=> inverse is

f'%28x%29=%281%2F2%29%28x%2B-sqrt%28x%5E2+-+20x+-+36%29%29