Inverses and domains?

Question

- Find the inverse of f.
- What are the domains and ranges of f and f^-1?

1. f(x) = (x+5)/(x-4)

My answer:

f^-1 (x) = (4x + 5) / (x-1)

Domain of f and range of f^-1 = (- inf , 4) U (4, inf)
Domain of f^-1 and range of f = (- inf , 1) U (1, inf)

2. f(x) = x^2 -2, x
My answer:

f^-1 (x) = sqrt (x + 2)

Domain of f and range of f^-1 = (- inf , 0 ]
Domain of f^-1 and range of f = [ -2 , 0 )

Am I right? Thanks.

Answer 1

Thanks for giving your answers!

#1 is correct.

For #2, the range of f is [-2, inf) (the graph of f is that part of the parabola y = x^2 - 2 to the left of the y-axis).

Also, the sqrt function is understood to be non-negative. So in order for the range of f^-1 to be (-inf,0], you would need to write

f^-1 (x) = -sqrt(x + 2)