Consider the function f(x)=x3+x+1 f ( x ) = x 3 + x + 1 Find the value (f−1)′(3) ( f − 1 ) ′ ( 3 ) Note that f(1) = 3.

Question

Consider the function

f(x)=x^3+x+1

Find the value 

(f^-1)’(3)

Note f(1)=3

Answer 1

When we take the inverse of a function, we are essentially just flipping the x's and y's around. So if f(1) = 3 (i.e., the point (1, 3) is on the curve of f(x)), then the point (3, 1) is on the curve of f^-1(x). That means that f^-1(3) = 1