Question

If f(x) = 37, what are the domain and range of the inverse function f-1(x)?

A) Domain: (-[infinity], [infinity]) Range: (0, [infinity])
B) Domain: (-[infinity], [infinity]) Range: (-[infinity], 0)
C) Domain: (0, [infinity]) Range: (-[infinity], [infinity])
D) Domain: (-[infinity], 0) Range: (-[infinity], [infinity])

Answer 1

The domain of the inverse function f-1(x), given f(x) = 37 and 0 ≤ x ≤ 20, is the single value {37}, and the range is [0, 20]. The provided answer options do not correctly reflect the domain and range of the inverse function.

Step-by-step explanation:

The student asked about finding the domain and range of the inverse function f-1(x) given that f(x) = 37. When f(x) is a constant function, it means that for all values of x in the domain, f(x) gives the same output, which is 37. Therefore, every input maps to the single output of 37, making the range of f(x) just the set {37}. Now, considering the inverse function f-1(x), the domain and range reverse roles. The domain of f-1(x) is the range of f(x), and the range of f-1(x) is the domain of f(x). Since f(x) is defined for 0 ≤ x ≤ 20, the domain of f-1(x) is {37}, and the range is [0, 20]. None of the provided options (A, B, C, D) correctly describe the domain and range of f-1(x).