Question

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)?

Answer 1

(4, 129), (129, 4)

Explanation:

With `f(x) = 2x^3 + 1`, we can easily assess
`f(4) = 2 * 4^3 + 1 = 2 * 64 + 1 = 129`

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

By definition, `f^(-1)(f(x)) = x`, hence `f^(-1)(129) = 4`. We can also manually do this:
`x = 2 * f^(-1)(x)^3 + 1 implies f^(-1)(x)^3 = 1/2 (x-1)`
`f^(-1)(x) = (1/2 (x-1))^(1/3)`
`f^(-1)(129) = (1/2(129-1))^(1/3) = (64)^(1/3) = 4`