Question

If f is a one-to-one function such that f(10) = 1, what is f-¹ (1)?

a. 1/10
b. 10 c. 1/1 d. 1
e. Not enough information is given.

Answer 1

For a one-to-one function where f(10) = 1, the inverse function f⁻¹(1) equals 10, since the inverse function reverses the mapping of f. b. 10 is correct.

Step-by-step explanation:

If f is a one-to-one function, and it is given that f(10) = 1, this means that for every x in the domain of f, there is a unique value of f(x) in the codomain, and vice versa. Consequently, the inverse function f⁻¹ takes each value of the codomain back to a unique value of the domain. Therefore, if f(10) = 1, then f⁻¹(1) = 10, because we are essentially 'reversing' the function f. Answer choice b. 10 is correct.