The discussion revolves around proving that two functions, f(x) = 9 - x^2 (for x ≥ 0) and g(x) = sqrt(9 - x), are inverses of each other. The participants are exploring the conditions under which two functions can be considered inverses.
The discussion is ongoing, with some participants providing guidance on simplification and emphasizing the need to also verify g(f(x)). There is an acknowledgment of the terminology used in the context of inverse functions.
There is a focus on ensuring the conditions for inverse functions are met, and participants are navigating through the implications of their calculations and definitions.
So close! Simplify the above.Physics-Pure said:Homework Statement
f(x) = 9-x^2, x ≥ 0. g(x) = sqrt (9-x)
Homework Equations
Two equations are inverses of each other if f(g(x)) = g(f(x)) = x.
The Attempt at a Solution
f(g(x)) = 9 - (sqrt (9-x))^2
= 9 - (9-x)