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Consider the function f(x) = |x – 1|/x2, then f (x) is
- a)increasing in (0, 1) ∪ (2, ∞)
- b)decreasing in (– ∞, 0) ∪ (1, 2)
- c)decreasing in (0, 2) ∪ (2, ∞)
- d)decreasing in (0, 1) ∪ (2, ∞)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the function f(x) = |x – 1|/x2, then f (x) isa)increasi...
Clearly, f (x) is continuous for all x ∈ R except at x = 0.
f '(x) > 0 ⇒ x< 0 or 1 < x < 2
f '(x) < 0 ⇒ 0 < x <1 or x > 2
Hence, f (x) is increasing in (-∞, 0)∪ (1, 2) and decreasing in (0, 1) ∪ (2,∞).
Most Upvoted Answer
Consider the function f(x) = |x – 1|/x2, then f (x) isa)increasi...
We cannot provide the full solution as the input for the absolute value function, |x|, is missing. However, we can provide some general information about the graph of the absolute value function.
The graph of f(x) = |x| is a V-shaped graph that passes through the origin. It reflects the input values of x across the y-axis to create a symmetric graph. The absolute value function is always positive or zero, so the graph is above the x-axis for positive values of x and below the x-axis for negative values of x.
If we have additional information about the input for the absolute value function, we can use that to determine the specific shape and location of the graph.
The graph of f(x) = |x| is a V-shaped graph that passes through the origin. It reflects the input values of x across the y-axis to create a symmetric graph. The absolute value function is always positive or zero, so the graph is above the x-axis for positive values of x and below the x-axis for negative values of x.
If we have additional information about the input for the absolute value function, we can use that to determine the specific shape and location of the graph.
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Consider the function f(x) = |x – 1|/x2, then f (x) isa)increasing in (0, 1) ∪ (2, ∞)b)decreasing in (– ∞, 0) ∪ (1, 2)c)decreasing in (0, 2) ∪ (2, ∞)d)decreasing in (0, 1) ∪ (2, ∞)Correct answer is option 'D'. Can you explain this answer?
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