which function has an inverse that is also a function?

$g(x) = 2x - 3$
$k(x) = -9x^2$
$f(x) = |x + 2|$
$w(x) = -20$

Question

which function has an inverse that is also a function?

$g(x) = 2x - 3$
$k(x) = -9x^2$
$f(x) = |x + 2|$
$w(x) = -20$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "One-to-One Functions", "Horizontal Line Test" ], "new_concepts": [], "current_concepts": [ "One-to-One Functions", "Horizontal Line Test", "Inverse Functions" ] } ## Analyze the condition for a function to have an inverse function $$ \text{A function has an inverse that is also a function if and only if it is a one-to-one function.} $$ ## Apply the horizontal line test to each option $$ \begin{aligned} &g(x) = 2x - 3 \quad \text{(Linear function with non-zero slope; passes the horizontal line test)} \ &k(x) = -9x^2 \quad \text{(Quadratic function; fails the horizontal line test)} \ &f(x) = |x + 2| \quad \text{(Absolute value function; fails the horizontal line test)} \ &w(x) = -20 \quad \text{(Constant function; fails the horizontal line test)} \end{aligned} $$ ## Identify the correct one-to-one function $$ g(x) = 2x - 3 $$

(A) $g(x) = 2x - 3$

(B) $k(x) = -9x^2$

(C) $f(x) = |x + 2|$

(D) $w(x) = -20$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "One-to-One Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the condition for a function to have an inverse function

Apply the horizontal line test to each option

Identify the correct one-to-one function

Answer: