Question

let f(x) = x^3 + 2x +1 assuming that the inverse exists and has a domain of
(−∞,∞), simplify

Answer 1

\[f[f ^{-1}(4)] = 4\]

Answer 2

why ?

Answer 3

because if the inverse exist,
f^-1 [f(x)] = x
just put x=4 here.

Answer 4

also 4 lies inside of range and domain, so its valid.

Answer 5

blah im dumb.. f^-1 is the inverse of f(x) .. sigh

Answer 6

and as long as x = all real numbers it be whatever is in the () right?

Answer 7

yup :)

Answer 8

sometimes... my brainlessness kills me