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The figure below shows the graph of a function f (x). How many solutions does the equation f ( f(x)) = 15 have?
- a)5
- b)6
- c)7
- d)8
- e)Cannot be determined from the given graph
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
The figure below shows the graph of a function f (x). How many solutio...
f ( f (x) = 15 when f (x) = 4 or f (x) = 12 in the given function. The graph given in the figure
becomes equal to 4 at 4 points and it becomes equal to 12 at 2 points in the figure. This gives us 6
points in the given figure when f (f (x) =15. However, the given function is continuous beyond the
part of it which is shown between –10 and +13 in the figure. Hence, we do not know how many
more solutions to f (f (x) = 15 would be there. Hence, Option (e) is the correct answer.
becomes equal to 4 at 4 points and it becomes equal to 12 at 2 points in the figure. This gives us 6
points in the given figure when f (f (x) =15. However, the given function is continuous beyond the
part of it which is shown between –10 and +13 in the figure. Hence, we do not know how many
more solutions to f (f (x) = 15 would be there. Hence, Option (e) is the correct answer.
Most Upvoted Answer
The figure below shows the graph of a function f (x). How many solutio...
Explanation:
To determine the number of solutions to the equation f(f(x)) = 15, we need to analyze the graph of the function f(x).
Step 1: Identify the Points where f(x) = 15
From the graph, we can see that f(x) intersects the horizontal line y = 15 at several points. Let's denote these points as A, B, C, D, E, F, G, H, I, J, K, L, and M.
Step 2: Analyze f(f(x))
To find f(f(x)), we need to evaluate the function f(x) at the x-values where f(x) = 15.
Step 3: Count the Number of Solutions
We can see that for each point where f(x) = 15, there is a corresponding value of x where f(f(x)) = 15. Therefore, the number of solutions to the equation f(f(x)) = 15 is equal to the number of points where f(x) = 15.
Step 4: Count the Number of Points where f(x) = 15
By visually inspecting the graph, we can count the number of points where f(x) = 15. In this case, it appears that there are more than 7 points of intersection between the graph of f(x) and the line y = 15. However, without specific coordinates or a more precise graph, we cannot determine the exact number of points.
Therefore, the correct answer is option E: Cannot be determined from the given graph.
To determine the number of solutions to the equation f(f(x)) = 15, we need to analyze the graph of the function f(x).
Step 1: Identify the Points where f(x) = 15
From the graph, we can see that f(x) intersects the horizontal line y = 15 at several points. Let's denote these points as A, B, C, D, E, F, G, H, I, J, K, L, and M.
Step 2: Analyze f(f(x))
To find f(f(x)), we need to evaluate the function f(x) at the x-values where f(x) = 15.
Step 3: Count the Number of Solutions
We can see that for each point where f(x) = 15, there is a corresponding value of x where f(f(x)) = 15. Therefore, the number of solutions to the equation f(f(x)) = 15 is equal to the number of points where f(x) = 15.
Step 4: Count the Number of Points where f(x) = 15
By visually inspecting the graph, we can count the number of points where f(x) = 15. In this case, it appears that there are more than 7 points of intersection between the graph of f(x) and the line y = 15. However, without specific coordinates or a more precise graph, we cannot determine the exact number of points.
Therefore, the correct answer is option E: Cannot be determined from the given graph.
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The figure below shows the graph of a function f (x). How many solutions does the equation f ( f(x)) = 15 have?a)5b)6c)7d)8e)Cannot be determined from the given graphCorrect answer is option 'E'. Can you explain this answer?
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