Consider the function f(x) = 2x^3+1. a) What is the ordered pair (4, f(4)) on the function? b) What is the ordered pair on the inverse relation that corresponds to the ordered pair from part a)?

1 Answer
Aug 14, 2018

(4, 129), (129, 4)

Explanation:

With f(x)=2x3+1, we can easily assess
f(4)=243+1=264+1=129

If we invert f, we can do this by hand or by definition.

By definition, f1(f(x))=x, hence f1(129)=4. We can also manually do this:
x=2f1(x)3+1f1(x)3=12(x1)
f1(x)=(12(x1))13
f1(129)=(12(1291))13=(64)13=4