Question Find the ordered pair of the function $F(x)$ if $(9,33)$ is an ordered pair of its inverse.

Studdy Solution

STEP 1

Assumptions
1. The ordered pair $(9,33)$ belongs to the inverse of the function $F(x)$ , denoted as $F^{-1}(x)$ .
2. We need to find an ordered pair that belongs to the function $F(x)$ itself.
3. The relationship between a function and its inverse involves swapping the x and y coordinates of the ordered pairs.

STEP 2

Understand the relationship between a function and its inverse. If $(a,b)$ is an ordered pair of a function $F(x)$ , then $(b,a)$ is an ordered pair of its inverse $F^{-1}(x)$ .

STEP 3

Apply the relationship to the given ordered pair $(9,33)$ . Since this pair belongs to the inverse $F^{-1}(x)$ , we can find the corresponding ordered pair for the function $F(x)$ by swapping the x and y coordinates.

STEP 4

Swap the coordinates of the given ordered pair $(9,33)$ to find the ordered pair for the function $F(x)$ .
$(x, y) = (9, 33) \Rightarrow (y, x) = (33, 9)$

STEP 5

Identify the correct ordered pair for the function $F(x)$ from the given options.
The ordered pair $(33,9)$ corresponds to the function $F(x)$ , which is option B.
The correct ordered pair of the function $F(x)$ is $(33,9)$ .

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