if (f(x)) and its inverse function, (f^{-1}(x)), are both plotted on the same coordinate plane, where is their point of intersection?

(0, 6)
(1, 4)
(2, 2)
(3, 0)

Question

if (f(x)) and its inverse function, (f^{-1}(x)), are both plotted on the same coordinate plane, where is their point of intersection?

(0, 6)
(1, 4)
(2, 2)
(3, 0)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Functions", "Inverse Functions", "Intersection of Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Inverse Functions", "Intersection of Inverse Functions" ] } ## Determine the equation of the linear function $$ \begin{aligned} &\text{y-intercept: } (0, 6) \ &\text{x-intercept: } (3, 0) \ &m = \frac{0 - 6}{3 - 0} = -2 \ &f(x) = -2x + 6 \end{aligned} $$ ## Find the intersection of the function and its inverse $$ \begin{aligned} &f(x) = x \ &-2x + 6 = x \ &3x = 6 \ &x = 2 \ &y = 2 \end{aligned} $$ ## Verify the intersection point $$ \begin{aligned} &(x, y) = (2, 2) \end{aligned} $$

(0, 6)

(1, 4)

(2, 2)

(3, 0)

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QUESTION IMAGE

Question

Explanation:

Determine the equation of the linear function

Find the intersection of the function and its inverse

Verify the intersection point

Answer: