Question

A function f is defined by f:x→x+10 over x-8,x not equal to 8.Find
the values of x for which f^-1(x)=x.

Answer 1

remember how I did the last one for you?

original:
y = (x+10)/(x-8)

inverse:
x = (y+10)/(y-8)
xy - 8x = y+10
xy - y = 8x + 10
y(x-1) = (8x+10)/(x-1)

f^-1 (x) = (8x+10)/(x-1)

so we want:
(8x+10)/(x-1) = x
x^2 - x = 8x + 10
x^2 - 9x - 10 = 0
(x-10)(x+1) = 0
x = 10 or x = -1

check:
f^-1 (10) = (80+10)/(10-1) = 90/9 = 10
f^-1 (-1) = (-8+10)/(-1-1) = 2/-2 = -1