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Math  /  Algebra

Question1. Complete the sentence below.
If the domain of a one-to-one function ff is [4,∞)[4, \infty), the range of its inverse, f−1f^{-1}, is \qquad .
If the domain of a one-to-one function ff is [4,∞)[4, \infty), the range of its inverse, f−1f^{-1}, is (1) \qquad (1) [4,∞)[4, \infty). (−∞,∞)(-\infty, \infty). (−∞,4](-\infty, 4].

Studdy Solution

STEP 1

1. We are given that f f is a one-to-one function.
2. The domain of f f is [4,∞)[4, \infty).
3. We need to determine the range of the inverse function f−1 f^{-1} .

STEP 2

1. Understand the relationship between the domain of a function and the range of its inverse.
2. Apply this understanding to determine the range of f−1 f^{-1} .

STEP 3

Recall that for a one-to-one function f f , the range of f f becomes the domain of its inverse f−1 f^{-1} , and the domain of f f becomes the range of f−1 f^{-1} .

STEP 4

Since the domain of f f is [4,∞)[4, \infty), this means that the range of f−1 f^{-1} is also [4,∞)[4, \infty).
The range of the inverse function f−1 f^{-1} is:
[4,∞) \boxed{[4, \infty)}

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