17
practice examMultiple Choice

Practice Exam

Question 17 • Algebraic Reasoning

Consider the inverse function. f inverse of x is equal to negative square root of x minus 2 end root Which conclusions can be drawn about f of x is equal to x squared plus 2 ? Choose three correct answers.

Answer
A
f of x has a y -intercept at the point open paren 0 comma 2 close paren .
B
f of x has an x -intercept of open paren 2 comma 0 close paren .
C
f of x has a restricted domain.
D
f of x has a limited range.
E
f of x has a maximum at the point open paren 0 comma 2 close paren .

Explanation

The inverse function is f⁻¹(x) = −√(x − 2), whose outputs are never positive. Those outputs become the domain of f, so f(x) = x² + 2 is restricted to x ≤ 0. It crosses the y-axis at (0, 2), and its range is [2, ∞), so the range is limited; (0, 2) is a minimum, not a maximum.

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