Calculus
posted by Mary .
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

if
f(x+2) = x^3+1, then replace x with x2 and you have
f(x2+2) = f(x) = (x2)^3 + 1
f^1(x) = ∛(x1) + 2
now just take the derivative of the inverse in the normal way. 
(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°
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