Math / Algebra

QuestionUse the graph of $y=f(x)$ in the figure to fill in the missing values. help (numbers) (a) $f(0)=$ $\square$ (b) $f(\square)=0$ (c) $f^{-1}(0)=$ $\square$ (d) $f^{-1}(\square)=0$ $\square$ (Click to enlarge)

Studdy Solution

STEP 1

1. We are interpreting a graph of the function $y = f(x)$ .
2. The graph provides visual information about the function values and their inverses.
3. We need to identify specific values based on the graph.

STEP 2

1. Determine the value of $f(0)$ .
2. Identify the x-value where $f(x) = 0$ .
3. Find the x-value for which $f^{-1}(0)$ is defined.
4. Determine the y-value where $f^{-1}(y) = 0$ .

STEP 3

To find $f(0)$ , locate the point on the graph where $x = 0$ and read the corresponding $y$ -value.
From the image description, the graph intersects the y-axis at approximately $y = 2$ .
Thus, $f(0) = 2$ .

STEP 4

To find $f(\square) = 0$ , locate the point where the graph intersects the x-axis.
The graph crosses the x-axis at approximately $x = -9$ .
Therefore, $f(-9) = 0$ .

STEP 5

To find $f^{-1}(0)$ , determine the x-value for which $f(x) = 0$ .
Since $f(x) = 0$ at $x = -9$ , it follows that $f^{-1}(0) = -9$ .

STEP 6

To find $f^{-1}(\square) = 0$ , determine the y-value for which $f^{-1}(y) = 0$ .
This implies finding the y-value where the graph intersects the x-axis at $x = 0$ .
Since $f(x)$ does not intersect the x-axis at $x = 0$ , we need to find the y-value where $f(0) = 0$ .
From the graph, $f(0) = 2$ , so $f^{-1}(2) = 0$ .
The filled values are: (a) $f(0) = 2$ (b) $f(-9) = 0$ (c) $f^{-1}(0) = -9$ (d) $f^{-1}(2) = 0$

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QuestionUse the graph of $y=f(x)$ in the figure to fill in the missing values. help (numbers) (a) $f(0)=$ $\square$ (b) $f(\square)=0$ (c) $f^{-1}(0)=$ $\square$ (d) $f^{-1}(\square)=0$ $\square$ (Click to enlarge)

Studdy Solution

STEP 1

1. We are interpreting a graph of the function $y = f(x)$ .
2. The graph provides visual information about the function values and their inverses.
3. We need to identify specific values based on the graph.

STEP 2

1. Determine the value of $f(0)$ .
2. Identify the x-value where $f(x) = 0$ .
3. Find the x-value for which $f^{-1}(0)$ is defined.
4. Determine the y-value where $f^{-1}(y) = 0$ .

STEP 3

To find $f(0)$ , locate the point on the graph where $x = 0$ and read the corresponding $y$ -value.
From the image description, the graph intersects the y-axis at approximately $y = 2$ .
Thus, $f(0) = 2$ .

STEP 4

To find $f(\square) = 0$ , locate the point where the graph intersects the x-axis.
The graph crosses the x-axis at approximately $x = -9$ .
Therefore, $f(-9) = 0$ .

STEP 5

To find $f^{-1}(0)$ , determine the x-value for which $f(x) = 0$ .
Since $f(x) = 0$ at $x = -9$ , it follows that $f^{-1}(0) = -9$ .

STEP 6

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QuestionUse the graph of y=f(x)y=f(x)y=f(x) in the figure to fill in the missing values. help (numbers) (a) f(0)=f(0)=f(0)= □\square□ (b) f(□)=0f(\square)=0f(□)=0 (c) f−1(0)=f^{-1}(0)=f−1(0)= □\square□ (d) f−1(□)=0f^{-1}(\square)=0f−1(□)=0 □\square□ (Click to enlarge)

Studdy Solution

STEP 1

1. We are interpreting a graph of the function y=f(x) y = f(x) y=f(x).2. The graph provides visual information about the function values and their inverses.3. We need to identify specific values based on the graph.

STEP 2

1. Determine the value of f(0) f(0) f(0).2. Identify the x-value where f(x)=0 f(x) = 0 f(x)=0.3. Find the x-value for which f−1(0) f^{-1}(0) f−1(0) is defined.4. Determine the y-value where f−1(y)=0 f^{-1}(y) = 0 f−1(y)=0.

STEP 3

To find f(0) f(0) f(0), locate the point on the graph where x=0 x = 0 x=0 and read the corresponding y y y-value.From the image description, the graph intersects the y-axis at approximately y=2 y = 2 y=2.Thus, f(0)=2 f(0) = 2 f(0)=2.

STEP 4

To find f(□)=0 f(\square) = 0 f(□)=0, locate the point where the graph intersects the x-axis.The graph crosses the x-axis at approximately x=−9 x = -9 x=−9.Therefore, f(−9)=0 f(-9) = 0 f(−9)=0.

STEP 5

To find f−1(0) f^{-1}(0) f−1(0), determine the x-value for which f(x)=0 f(x) = 0 f(x)=0.Since f(x)=0 f(x) = 0 f(x)=0 at x=−9 x = -9 x=−9, it follows that f−1(0)=−9 f^{-1}(0) = -9 f−1(0)=−9.

STEP 6

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QuestionUse the graph of $y=f(x)$ in the figure to fill in the missing values. help (numbers) (a) $f(0)=$ $\square$ (b) $f(\square)=0$ (c) $f^{-1}(0)=$ $\square$ (d) $f^{-1}(\square)=0$ $\square$ (Click to enlarge)

1. We are interpreting a graph of the function $y = f(x)$ .
2. The graph provides visual information about the function values and their inverses.
3. We need to identify specific values based on the graph.

1. Determine the value of $f(0)$ .
2. Identify the x-value where $f(x) = 0$ .
3. Find the x-value for which $f^{-1}(0)$ is defined.
4. Determine the y-value where $f^{-1}(y) = 0$ .

To find $f(0)$ , locate the point on the graph where $x = 0$ and read the corresponding $y$ -value.
From the image description, the graph intersects the y-axis at approximately $y = 2$ .
Thus, $f(0) = 2$ .

To find $f(\square) = 0$ , locate the point where the graph intersects the x-axis.
The graph crosses the x-axis at approximately $x = -9$ .
Therefore, $f(-9) = 0$ .

To find $f^{-1}(0)$ , determine the x-value for which $f(x) = 0$ .
Since $f(x) = 0$ at $x = -9$ , it follows that $f^{-1}(0) = -9$ .