Question

Consider the function f(x) = x^2 – 331. Chivonne claims a domain restriction x ≥ 0 produces the inverse function f–1(x) = √ x - 331 .

Which statement describes whether Chivonne is correct?

A) The expression for f–1(x) is correct, but the domain restriction is not.
B) The domain restriction is correct, but the expression for f–1(x) is not.
C) Both the expression for f–1(x) and the domain restriction are correct.
D) Neither the domain restriction nor the expression for f–1(x) is correct.

Answer 1

Answer:

The correct option is;

D) Neither the domain restriction nor the expression for f⁻¹(x) is correct

Step-by-step explanation:

The given function can be written as follows;

f(x) = x² - 331

The inverse of the function f(x), which is f⁻¹(x), can be found as follows;

Let f(x) = x² - 331 = y, we have;

f(x) + 331 = x²

x = √(f(x) + 331)

We replace x with f⁻¹(x) and f(x) with x, to get;

f⁻¹(x) = √(x + 331)

We note that the domain of the inverse function will include values from x ≥ -331, and the correct inverse function √(x + 331) ≠ √x - 331

Therefore, we have that neither the domain restriction nor the expression for f⁻¹(x) is correct.

Answer 2

Answer:

B) The domain restriction is correct, but the expression for f–1(x) is not.

The ANSWER IS NOT C as "oeerivona" stated

Step-by-step explanation:

The answer is B on Edge.   (VERIFIED Edge Answer)

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