6
QuizMultiple Choice

Function Inverses — Quiz

Question 6 • Mathematics III

Which statement verifies that f of x and g of x are inverses of each other?

Answer
A
f of g of x is equal to x and g of f of x is equal to negative x
B
f of g of x is equal to x
C
f of g of x is equal to x and g of f of x is equal to x
D
f of g of x is equal to 1 over g of f of x

Explanation

Two functions are inverses when composing them in either order gives the original input: f(g(x)) = x and g(f(x)) = x. Choice A states both required identities. Choice C checks only one composition, which is not enough to verify that the functions are inverses.

AI-written and checked against the verified answer.

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