Question

Hello I need help with this excersise of derivative of a inverse function. The excersise says:
If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] .
I don't know which is the function f, they only give me f (x+2) and I don't understand how to get f
Please help

Answer 1

if
f(x+2) = x^3+1, then replace x with x-2 and you have
f(x-2+2) = f(x) = (x-2)^3 + 1
f^-1(x) = ∛(x-1) + 2

now just take the derivative of the inverse in the normal way.

Answer 2

(a) Find an angle between
0
and
2π
that is coterminal with
−7π2
.
(b) Find an angle between
0°
and
360°
that is coterminal with
586°