Question

Consider the function f(x) = x2 – 331. Chivonne claims a domain restriction x ≥ 0 produces the inverse function f–1(x) = StartRoot x minus 331 EndRoot . Which statement describes whether Chivonne is correct? The expression for f–1(x) is correct, but the domain restriction is not. The domain restriction is correct, but the expression for f–1(x) is not. Both the expression for f–1(x) and the domain restriction are correct. Neither the domain restriction nor the expression for f–1(x) is correct.

Answer 1

Answer: B

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

Explanation:

Answer 2

The correct option is;

The domain restriction is correct but the expression for f⁻¹(x) is not

Explanation:

The expression for the function is given as follows;

f(x) = x² - 331

The inverse function suggested = f⁻¹(x) = √(x-331)

The domain restriction is x ≥ 0

The inverse function if given as follows;

y = x² - 331 (Interchange x and y to get)

x = y² - 331

x + 331 = y²

y = ±√(x + 331)

Given that the domain restriction has been put as x ≥ 0, we select the + case to give;

f⁻¹(x) = √(x + 331)

Therefore, the domain restriction is correct but the expression for f⁻¹(x) is not.